|
|
|
- Duane Davis
- 5 years ago
- Views:
Transcription
1 Page 1 of 1-7 Equations Teks Focus TEKS (2)(B) Derive and use the distance, slope, and midpoint formulas to verify geometric relationships, including congruence of segments and parallelism or perpendicularity of pairs of lines. TEKS (1)(D) Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate. Additional TEKS (1)(E) Vocabulary Point-slope form The point-slope form for a nonvertical line with slope m and through point (x 1, y 1) is y y 1 = m(x x 1). Slope the ratio of a line's vertical change (rise) to its corresponding horizontal change (run) between any two points in the coordinate plane Slope-intercept form The slope-intercept form of the equation of a nonvertical line is y = mx + b, where m is the slope and b is the y-intercept. Implication a conclusion that follows from previously stated ideas or reasoning without being explicitly stated Representation a way to display or describe information. You can use a representation to present mathematical ideas and data. ESSENTIAL UNDERSTANDING You can graph a line and write its equation when you know certain facts about the line, such as its slope and a point on the line. take note Key Concept Slope Definition Symbols Diagram The slope m of a line is the ratio of the vertical change (rise) to the horizontal change (run) between any two points. A line contains the points (x 1, y 1) and (x 2, y 2). rise y m = run = 2 y 1 x 2 x 1 The slope of a line can be positive, negative, zero, or undefined. The sign of the slope tells you whether the line rises or falls to the right. A slope of zero tells you that the line is horizontal. An undefined slope tells you that the line is vertical. PearsonTEXAS.com Page 12 Copyright 2016 Pearson Education, Inc. or its affiliate(s). All rights reserved. Privacy Policy Terms of Use Rights and Permissions
2 Page 1 of 2 take note Key Concept Forms of Linear Equations Definition Symbols The slope-intercept form of an equation of a nonvertical line is y = mx + b, where m is the slope and b is the y-intercept. The point-slope form of an equation of a nonvertical line is y y 1 = m(x x 1), where m is the slope and (x 1, y 1) is a point on the line. Problem 1 TEKS Process Standard (1)(D) Deriving the Slope Formula Derive a formula that you can use to find the slope of a line. The slope of a line is the ratio of the vertical change to the horizontal change between any two points. Step 1 Mark points (x 1, y 1) and (x 2, y 2), and draw a line through them. Step 2 Since the y-coordinates correspond to values on a vertical number line (y-axis), use the definition of distance between two points to find the vertical change. The vertical change is the difference between y 2 and y 1, or y 2 y 1. Step Since the x-coordinates correspond to values on a horizontal number line (x-axis), use the definition of distance between two points to find the horizontal change. The horizontal change is the difference between x 2 and x 1, or x 2 x 1. Step 4 Find the slope m by determining the ratio of vertical change to horizontal change. So the slope formula is m = y 2 y 1. x 2 x 1 Problem 2 Think What reason can you give for drawing a line through points (x 1, y 1) and (x 2, y 2) in Step 1? Postulate 1-1 states that through any two points, there is exactly one line. Finding Slopes of Lines A What is the slope of line b? m = 2 ( 2) 1 4 = 4 5 = 4 5 B What is the slope of line d? m = 0 ( 2) 4 4 = 2 0 Undefined Plan How do you know which numbers go where in a formula? For slope, you can choose either point's y-coordinate as y 2. Just be sure to use the same point's x-coordinate as x 2.
3 Page 2 of 2 Page 124 Copyright 2016 Pearson Education, Inc. or its affiliate(s). All rights reserved. Privacy Policy Terms of Use Rights and Permissions
4 Page 1 of 1 Problem TEKS Process Standard (1)(E) Graphing Lines 2 A What is the graph of y = x +1? The equation is in slope-intercept form, y = mx + b. The slope m is, and the y-intercept b is 1. 2 Plan What do you do first? Determine which form of linear equation you have. Then use the equation to identify the slope and a starting point. d B What is the graph of y = 2(x + )? The equation is in point-slope form, y y 1 = m(x x 1). The slope m is 2, and a point (x 1, y 1) on the line is (, ). d Think What do you do when the slope is not a fraction? A rise always needs a run. So write the integer as a fraction with 1 as the denominator. PearsonTEXAS.com Page 125 Copyright 2016 Pearson Education, Inc. or its affiliate(s). All rights reserved. Privacy Policy Terms of Use Rights and Permissions
5 Page 1 of 2 Problem 4 Writing Equations of Lines A What is an equation of the line with slope and y-intercept 5? Plan Which linear equation form should you use? B What is an equation of the line through ( 1, 5) with slope 2? When you know the slope and the y-intercept, use slopeintercept form. When you know the slope and a point on the line, use point-slope form. Problem 5 Using Two Points to Write an Equation What is an equation of the line at the right? Plan What is the first thing you need to know? It doesn't matter yet what form of linear equation you plan to use. You'll need the slope for both slope-intercept form and point-slope form. Think Write y Start by finding the slope m of the line through the given points. m= 2 y 1 5 ( 1) 6 x 2 x 1 = = ( 2) 5 You have the slope, and you know two points on the line. Use point-slope form. y y 1 = m(x x 1) 6 Use either point for (x 1, y 1). For example, you can use (, 5). y 5= (x ) 5 Problem 6 Writing Equations of Horizontal and Vertical Lines What are the equations for the horizontal and vertical lines through (2, 4)? Every point on the horizontal line through (2, 4) has a y-coordinate of 4. The equation of the line is y = 4. It crosses the y-axis at (0, 4). Every point on the vertical line through (2, 4) has an x-coordinate of 2. The equation of the line is x = 2. It crosses the x-axis at (2, 0). Think How is this different from writing other linear equations? You don't need the slope. Just locate the point where the line crosses the x-axis (for vertical) or y-axis (for horizontal).
6 Page 1 of 2 PRACTICE and APPLICATION EXERCISES Find the slope of the line passing through the given points. Scan page for a Virtual Nerd tutorial video. 1. For additional support when completing your homework, go to PearsonTEXAS.com. 2.. (, 7), ( 1, 4) 4. (, 2), ( 6, 2) 5. (5, 9), (5, 6) Graph each line. 6. y = x y = x y = (x ) 9. y 1 = (x + 2) Use the given information to write an equation of each line slope, passes through ( 2, 6) 11. slope, passes through (4, 1) 12.
7 Page 2 of passes through (0, 5) and (5, 8) 15. passes through (6, 2) and (2, 4) 16. Use Multiple Representations to Communicate Mathematical Ideas (1)(D) Derive the slope formula. Include a graph as part of your answer. For Exercises 17 and 18, write the equation of the horizontal and vertical lines though the given point. 17. (4, 7) 18. (0, 1) 19. Write equations for three lines that contain the point (5, 6). Graph each pair of lines. Then find their point of intersection. 20. y = 4, x = x = 0, y = x = 1, y = PearsonTEXAS.com Page 127 Copyright 2016 Pearson Education, Inc. or its affiliate(s). All rights reserved. Privacy Policy Terms of Use Rights and Permissions
8 Page 1 of 2 2. What is the slope of the x-axis? Explain. Write an equation for the x-axis. 24. What is the slope of the y-axis? Explain. Write an equation for the y-axis. 25. Analyze Mathematical Relationships (1)(F) You want to construct a funbox at a local skate park. The skate park's safety regulations allow for the ramp on the funbox to have a maximum slope of. If you use the funbox plan at the right, can you build the ramp to meet the safety regulations? Explain Write each equation in slope-intercept form. 26. y 5 = 2(x + 2) 27. y + 2 = (x 4) 28. x + 2y = 10 1 STEM 29. Apply Mathematics (1)(A) The equation P = d +1represents the pressure P in atmospheres a scuba diver feels d feet below the surface of the water. a. What is the slope of the line? What does the slope represent in this situation? b. What is the y-intercept (P-intercept)? What does it represent in this situation? 0. Analyze Mathematical Relationships (1)(F) The x-intercept of a line is 2, and the y-intercept is 4. Use this information to write an equation for the line. 1. Connect Mathematical Ideas (1)(F) The vertices of a triangle are A(0, 0), B(2, 5), and C(4, 0). a. Write an equation for the line through A and B. b. Write an equation for the line through B and C. c. Compare the slopes and the y-intercepts of the two lines. Do the three points lie on one line? Justify your answer. 2. (5, 6), (, 2), (6, 8). ( 2, 2), (4, 4), (0, 0) 4. (5, 4), (2, ), ( 1, 10) TEXAS Test Practice 5. AB has endpoints A(8, k) and B(7, ). The slope of AB is 5. What is k? A. 1 B. 2 C. 5 D Two angles of a triangle measure 68 and 54. What is the measure of the third angle? F 14 G. 58 H. 122 J One of the angles in a certain linear pair is acute. Your friend says the other angle must be obtuse. Is your friend's conjecture reasonable? Explain. Page 128
4.4 Slope and Graphs of Linear Equations. Copyright Cengage Learning. All rights reserved.
4.4 Slope and Graphs of Linear Equations Copyright Cengage Learning. All rights reserved. 1 What You Will Learn Determine the slope of a line through two points Write linear equations in slope-intercept
ACT Coordinate Geometry Review
ACT Coordinate Geometry Review Here is a brief review of the coordinate geometry concepts tested on the ACT. Note: there is no review of how to graph an equation on this worksheet. Questions testing this
Chapter 9 Linear equations/graphing. 1) Be able to graph points on coordinate plane 2) Determine the quadrant for a point on coordinate plane
Chapter 9 Linear equations/graphing 1) Be able to graph points on coordinate plane 2) Determine the quadrant for a point on coordinate plane Rectangular Coordinate System Quadrant II (-,+) y-axis Quadrant
LINEAR EQUATIONS IN TWO VARIABLES
LINEAR EQUATIONS IN TWO VARIABLES What You Should Learn Use slope to graph linear equations in two " variables. Find the slope of a line given two points on the line. Write linear equations in two variables.
Name Period GEOMETRY CHAPTER 3 Perpendicular and Parallel Lines Section 3.1 Lines and Angles GOAL 1: Relationship between lines
Name Period GEOMETRY CHAPTER 3 Perpendicular and Parallel Lines Section 3.1 Lines and Angles GOAL 1: Relationship between lines Two lines are if they are coplanar and do not intersect. Skew lines. Two
Algebra & Trig. 1. , then the slope of the line is given by
Algebra & Trig. 1 1.4 and 1.5 Linear Functions and Slope Slope is a measure of the steepness of a line and is denoted by the letter m. If a nonvertical line passes through two distinct points x, y 1 1
Lesson 16: The Computation of the Slope of a Non Vertical Line
++ Lesson 16: The Computation of the Slope of a Non Vertical Line Student Outcomes Students use similar triangles to explain why the slope is the same between any two distinct points on a non vertical
CHAPTER 3. Parallel & Perpendicular lines
CHAPTER 3 Parallel & Perpendicular lines 3.1- Identify Pairs of Lines and Angles Parallel Lines: two lines are parallel if they do not intersect and are coplaner Skew lines: Two lines are skew if they
Angles formed by Transversals
Section 3-1: Parallel Lines and Transversals SOL: None Objectives: Identify the relationships between two lines or two planes Name angles formed by a pair of lines and a transversal Vocabulary: Parallel
Chapter 9. Conic Sections and Analytic Geometry. 9.1 The Ellipse. Copyright 2014, 2010, 2007 Pearson Education, Inc.
Chapter 9 Conic Sections and Analytic Geometry 9.1 The Ellipse Copyright 2014, 2010, 2007 Pearson Education, Inc. 1 Objectives: Graph ellipses centered at the origin. Write equations of ellipses in standard
Determine the intercepts of the line and ellipse below: Definition: An intercept is a point of a graph on an axis. Line: x intercept(s)
Topic 1 1 Intercepts and Lines Definition: An intercept is a point of a graph on an axis. For an equation Involving ordered pairs (x, y): x intercepts (a, 0) y intercepts (0, b) where a and b are real
6.1 Slope of a Line Name: Date: Goal: Determine the slope of a line segment and a line.
6.1 Slope of a Line Name: Date: Goal: Determine the slope of a line segment and a line. Toolkit: - Rate of change - Simplifying fractions Main Ideas: Definitions Rise: the vertical distance between two
4 The Cartesian Coordinate System- Pictures of Equations
The Cartesian Coordinate System- Pictures of Equations Concepts: The Cartesian Coordinate System Graphs of Equations in Two Variables x-intercepts and y-intercepts Distance in Two Dimensions and the Pythagorean
In this section, we find equations for straight lines lying in a coordinate plane.
2.4 Lines Lines In this section, we find equations for straight lines lying in a coordinate plane. The equations will depend on how the line is inclined. So, we begin by discussing the concept of slope.
Outcome 7 Review. *Recall that -1 (-5) means
Outcome 7 Review Level 2 Determine the slope of a line that passes through A(3, -5) and B(-2, -1). Step 1: Remember that ordered pairs are in the form (x, y). Label the points so you can substitute into
Ch. 6 Linear Functions Notes
First Name: Last Name: Block: Ch. 6 Linear Functions Notes 6.1 SLOPE OF A LINE Ch. 6.1 HW: p. 9 #4 1, 17,,, 8 6. SLOPES OF PARALLEL AND PERPENDICULAR LINES 6 Ch. 6. HW: p. 49 # 6 odd letters, 7 0 8 6.
Study Guide: Slope and Linear Equations
Rates and Unit Rates A rate is a proportional relationship between two quantities. Unit rate is a rate where the second quantity is 1. Example: Pauline can mow 35 square feet of lawn is 2.5 minutes. (this
Use smooth curves to complete the graph between and beyond the vertical asymptotes.
5.3 Graphs of Rational Functions Guidelines for Graphing Rational Functions 1. Find and plot the x-intercepts. (Set numerator = 0 and solve for x) 2. Find and plot the y-intercepts. (Let x = 0 and solve
Geometry Vocabulary Book
Geometry Vocabulary Book Units 2-4 Page 1 Unit 2 General Geometry Point Characteristics: Line Characteristics: Plane Characteristics: RELATED POSTULATES: Through any two points there exists exactly one
Math 1023 College Algebra Worksheet 1 Name: Prof. Paul Bailey September 22, 2004
Math 1023 College Algebra Worksheet 1 Name: Prof. Paul Bailey September 22, 2004 Every vertical line can be expressed by a unique equation of the form x = c, where c is a constant. Such lines have undefined
Solving Equations and Graphing
Solving Equations and Graphing Question 1: How do you solve a linear equation? Answer 1: 1. Remove any parentheses or other grouping symbols (if necessary). 2. If the equation contains a fraction, multiply
10 GRAPHING LINEAR EQUATIONS
0 GRAPHING LINEAR EQUATIONS We now expand our discussion of the single-variable equation to the linear equation in two variables, x and y. Some examples of linear equations are x+ y = 0, y = 3 x, x= 4,
Tasks for this target will ask students to graph one or more proportional relationships and connect the unit rate(s) to the context of the problem.
Grade 8 Math C1 TC Claim 1: Concepts and Procedures Students can explain and apply mathematical concepts and carry out mathematical procedures with precision and fluency. Content Domain: Expressions and
CH 54 SPECIAL LINES. Ch 54 Special Lines. Introduction
479 CH 54 SPECIAL LINES Introduction Y ou may have noticed that all the lines we ve seen so far in this course have had slopes that were either positive or negative. You may also have observed that every
3.1 parallel lines and transversals
VOCAB Parallel lines- 3.1 parallel lines and transversals Skew lines- Parallel planes- Transversal- Interior < s Transversal Angle Pair Relationships Exterior < s Same side Interior < s (consecutive interiors
E. Slope-Intercept Form and Direct Variation (pp )
and Direct Variation (pp. 32 35) For any two points, there is one and only one line that contains both points. This fact can help you graph a linear equation. Many times, it will be convenient to use the
Appendix M TERMINOLOGY. Slope of a Line. Slope. Undefined Slope. Slope-Intercept Form
Appendices : Slope of a Line TERMINOLOGY For each of the following terms, provide ) a definition in our own words, 2) the formal definition (as provided b our text or instructor), and ) an example of the
Chapter 3 Linear Equations in Two Variables
Chapter Linear Equations in Two Variables. Check Points. 6. x y x ( x, y) y ( ) 6, 6 y ( ), 0 y (0) 0, y () 0,0 y (),. E(, ) F(,0) G (6,0). a. xy 9 ( ) 9 69 9 9, true (, ) is a solution. b. xy 9 () 9 99
Geometry. Unit 3 Parallel and Perpendicular Lines. Name:
Geometry Unit 3 Parallel and Perpendicular Lines Name: 1 Geometry Chapter 3 Parallel and Perpendicular Lines ***In order to get full credit for your assignments they must me done on time and you must SHOW
Chapter 2: Functions and Graphs Lesson Index & Summary
Section 1: Relations and Graphs Cartesian coordinates Screen 2 Coordinate plane Screen 2 Domain of relation Screen 3 Graph of a relation Screen 3 Linear equation Screen 6 Ordered pairs Screen 1 Origin
Graphs, Linear Equations and Functions
Graphs, Linear Equations and Functions There are several ways to graph a linear equation: Make a table of values Use slope and y-intercept Use x and y intercepts Oct 5 9:37 PM Oct 5 9:38 PM Example: Make
Math 154 :: Elementary Algebra
Math :: Elementary Algebra Section. Section. Section. Section. Section. Math :: Elementary Algebra Section. The Rectangular (Cartesian) Coordinate System. The variable x usually represents the independent
Chapter 7, Part 1B Equations & Functions
Chapter 7, Part 1B Equations & Functions Fingerstache Fingerstaches cost $7 per box. Copy and complete the table to find the cost of 2, 3, and 4 boxes. Number of Boxes Multiply by 7 Cost 1 1 x 7 $7 2 3
Block: Date: Name: REVIEW Linear Equations. 7.What is the equation of the line that passes through the point (5, -3) and has a slope of -3?
Name: REVIEW Linear Equations 1. What is the slope of the line y = -2x + 3? 2. Write the equation in slope-intercept form. Block: Date: 7.What is the equation of the line that passes through the point
Find the coordinates of the midpoint of a segment having the given endpoints.
G.(2) Coordinate and transformational geometry. The student uses the process skills to understand the connections between algebra and geometry and uses the one- and two-dimensional coordinate systems to
Find the equation of a line given its slope and y-intercept. (Problem Set exercises 1 6 are similar.)
Directions Each problem below is similar to the example with the same number in your textbook. After reading through an example in your textbook, or watching one of the videos of that example on MathTV,
Slopes of of Parallel and and Perpendicular Lines Lines Holt Algebra 1
5-8 Slopes of of Parallel and and Lines Warm Up Lesson Presentation Lesson Quiz Bell Quiz 5-8 Find the reciprocal. 1. 2 2. 1 pt 1 pt 1 pt 3. 2 pts 2 pts 2 pts Find the slope of the line that passes through
Student Exploration: Standard Form of a Line
Name: Date: Student Exploration: Standard Form of a Line Vocabulary: slope, slope-intercept form, standard form, x-intercept, y-intercept Prior Knowledge Questions (Do these BEFORE using the Gizmo.) 1.
Vocabulary slope, parallel, perpendicular, reciprocal, negative reciprocal, horizontal, vertical, rise, run (earlier grades)
Slope Reporting Category Reasoning, Lines, and Transformations Topic Exploring slope, including slopes of parallel and perpendicular lines Primary SOL G.3 The student will use pictorial representations,
Study Guide: Slope and Linear Equations
Rates and Unit Rates A rate is a proportional relationship between two quantities. Unit rate is a rate where the second quantity is 1. Example: Pauline can mow 35 square feet of lawn is 2.5 minutes. (this
Review for Mastery. Identifying Linear Functions
Identifying Linear Functions You can determine if a function is linear by its graph, ordered pairs, or equation. Identify whether the graph represents a linear function. Step 1: Determine whether the graph
Lesson 3A. Opening Exercise. Identify which dilation figures were created using r = 1, using r > 1, and using 0 < r < 1.
: Properties of Dilations and Equations of lines Opening Exercise Identify which dilation figures were created using r = 1, using r > 1, and using 0 < r < 1. : Properties of Dilations and Equations of
Page 1 of 17 Name: Which graph does not represent a function of x? What is the slope of the graph of the equation y = 2x -? 2 2x If the point ( 4, k) is on the graph of the equation 3x + y = 8, find the
Section 1.3. Slope of a Line
Slope of a Line Introduction Comparing the Steepness of Two Objects Two ladders leaning against a building. Which is steeper? We compare the vertical distance from the base of the building to the ladder
MS Algebra A-S-ID-7 Ch. 5.5a Find Slope Given Two Points. Mr. Deyo Find Slope and Rate of Change
MS Algebra A-S-ID-7 Ch. 5.5a Find Slope Given Two Points Mr. Deyo Find Slope and Rate of Change Title: 5.5a Find Slope Given Two Points Date: Learning Target By the end of the period, I will find the slope
You MUST know the big 3 formulas!
Name 3-13 Review Geometry Period Date Unit 3 Lines and angles Review 3-1 Writing equations of lines. Determining slope and y intercept given an equation Writing the equation of a line given a graph. Graphing
Graphing - Slope-Intercept Form
2.3 Graphing - Slope-Intercept Form Objective: Give the equation of a line with a known slope and y-intercept. When graphing a line we found one method we could use is to make a table of values. However,
Graphing Lines with a Table
Graphing Lines with a Table Select (or use pre-selected) values for x Substitute those x values in the equation and solve for y Graph the x and y values as ordered pairs Connect points with a line Graph
ACTIVITY: Finding the Slope of a Line
. Slope of a Line describe the line? How can ou use the slope of a line to Slope is the rate of change between an two points on a line. It is the measure of the steepness of the line. To find the slope
Pearson's Ramp-Up Mathematics
Introducing Slope L E S S O N CONCEPT BOOK See pages 7 8 in the Concept Book. PURPOSE To introduce slope as a graphical form of the constant of proportionality, k. The lesson identifies k as the ratio
Section 1.3. Slope formula: If the coordinates of two points on the line are known then we can use the slope formula to find the slope of the line.
MATH 11009: Linear Functions Section 1.3 Linear Function: A linear function is a function that can be written in the form f(x) = ax + b or y = ax + b where a and b are constants. The graph of a linear
2.3 Quick Graphs of Linear Equations
2.3 Quick Graphs of Linear Equations Algebra III Mr. Niedert Algebra III 2.3 Quick Graphs of Linear Equations Mr. Niedert 1 / 11 Forms of a Line Slope-Intercept Form The slope-intercept form of a linear
Analytic Geometry ةيليلحتلا ةسدنھلا
Analytic Geometry الھندسة التحليلية نظام اإلحداثيات الديكارتي 1-1 Cartesian Coordinate System The Cartesian coordinate system, or the rectangular coordinate system, is a geometrical system that is used
Analytic Geometry. The x and y axes divide the Cartesian plane into four regions called quadrants.
Analytic Geometry الھندسة التحليلية نظام اإلحداثيات الديكارتي 1-1 Cartesian Coordinate System The Cartesian coordinate system, or the rectangular coordinate system, is a geometrical system that is used
1.7 Parallel and Perpendicular Lines
Section 1.7 Parallel and Perpendicular Lines 11 Eplaining the Concepts 17. Name the five forms of equations of lines given in this section. 18. What tpe of line has one -intercept, but no -intercept? 19.
Outcome 9 Review Foundations and Pre-Calculus 10
Outcome 9 Review Foundations and Pre-Calculus 10 Level 2 Example: Writing an equation in slope intercept form Slope-Intercept Form: y = mx + b m = slope b = y-intercept Ex : Write the equation of a line
Section 3.5. Equations of Lines
Section 3.5 Equations of Lines Learning objectives Use slope-intercept form to write an equation of a line Use slope-intercept form to graph a linear equation Use the point-slope form to find an equation
MA Lesson 16 Sections 2.3 and 2.4
MA 1500 Lesson 16 Sections.3 and.4 I Piecewise Functions & Evaluating such Functions A cab driver charges $4 a ride for a ride less than 5 miles. He charges $4 plus $0.50 a mile for a ride greater than
y-intercept remains constant?
1. The graph of a line that contains the points ( 1, 5) and (4, 5) is shown below. Which best represents this line if the slope is doubled and the y-intercept remains constant? F) G) H) J) 2. The graph
A slope of a line is the ratio between the change in a vertical distance (rise) to the change in a horizontal
The Slope of a Line (2.2) Find the slope of a line given two points on the line (Objective #1) A slope of a line is the ratio between the change in a vertical distance (rise) to the change in a horizontal
Slope. Plug In. Finding the Slope of a Line. m 5 1_ 2. The y-intercept is where a line
LESSON Slope Plug In Finding the Slope of a Line The slope of a line is the ratio of the change in the -values to the change in the corresponding -values. 0 7 8 change in -values Slope change in -values
Warm-Up. Complete the second homework worksheet (the one you didn t do yesterday). Please begin working on FBF010 and FBF011.
Warm-Up Complete the second homework worksheet (the one you didn t do yesterday). Please begin working on FBF010 and FBF011. You have 20 minutes at the beginning of class to work on these three tasks.
Math + 4 (Red) SEMESTER 1. { Pg. 1 } Unit 1: Whole Number Sense. Unit 2: Whole Number Operations. Unit 3: Applications of Operations
Math + 4 (Red) This research-based course focuses on computational fluency, conceptual understanding, and problem-solving. The engaging course features new graphics, learning tools, and games; adaptive
Mathematics Success Grade 8
Mathematics Success Grade 8 T429 [OBJECTIVE] The student will solve systems of equations by graphing. [PREREQUISITE SKILLS] solving equations [MATERIALS] Student pages S207 S220 Rulers [ESSENTIAL QUESTIONS]
8.2 Slippery Slopes. A Solidify Understanding Task
7 8.2 Slippery Slopes A Solidify Understanding Task CC BY https://flic.kr/p/kfus4x While working on Is It Right? in the previous module you looked at several examples that lead to the conclusion that the
Section 2-4: Writing Linear Equations, Including Concepts of Parallel & Perpendicular Lines + Graphing Practice
Section 2-4: Writing Linear Equations, Including Concepts of Parallel & Perpendicular Lines + Graphing Practice Name Date CP If an equation is linear, then there are three formats typically used to express
Algebra Success. LESSON 16: Graphing Lines in Standard Form. [OBJECTIVE] The student will graph lines described by equations in standard form.
![Algebra Success. LESSON 16: Graphing Lines in Standard Form. [OBJECTIVE] The student will graph lines described by equations in standard form.](/thumbs/93/113878239.jpg "Algebra Success. LESSON 16: Graphing Lines in Standard Form. [OBJECTIVE] The student will graph lines described by equations in standard form.")
T328 [OBJECTIVE] The student will graph lines described by equations in standard form. [MATERIALS] Student pages S125 S133 Transparencies T336, T338, T340, T342, T344 Wall-size four-quadrant grid [ESSENTIAL
Parallel Postulate. Perpendicular Postulate PARALLEL AND SKEW LINES WITH PARALLEL PLANES. Lines m and n are. Lines m and k are. Planes T and U are.
Unit 6: Parallel and Perpendicular Lines Lesson 6.1: Identify Pairs of Lines and Angles Lesson 3.1 from textbook Objectives Identify relationships between lines such as parallel and skew. Understand and
4.4 Equations of Parallel and Perpendicular
www.ck12.org Chapter 4. Determining Linear Equations 4.4 Equations of Parallel and Perpendicular Lines Learning Objectives Determine whether lines are parallel or perpendicular. Write equations of perpendicular
Parallel and Perpendicular Lines on the Coordinate Plane
Did You Find a Parking Space? Parallel and Perpendicular Lines on the Coordinate Plane 1.5 Learning Goals Key Term In this lesson, you will: Determine whether lines are parallel. Identify and write the
3-5 Slopes of Lines. Warm Up Lesson Presentation Lesson Quiz. Holt McDougal Geometry
3-5 Slopes of Lines Warm Up Lesson Presentation Lesson Quiz Geometry Warm Up Find the value of m. 1. 2. 3. 4. undefined 0 Objectives Find the slope of a line. Use slopes to identify parallel and perpendicular
Chapter 3 Parallel and Perpendicular Lines
Chapter 3 Parallel and Perpendicular Lines Parallel Lines Lines Parallel Symbol: Perpendicular Lines Lines that Perpendicular Symbol: Postulate 13: Parallel Postulate For any and a not on the line, there
Lesson 7 Slope-Intercept Formula
Lesson 7 Slope-Intercept Formula Terms Two new words that describe what we've been doing in graphing lines are slope and intercept. The slope is referred to as "m" (a mountain has slope and starts with
Characteristics of Linear Relations
HW Mark: 10 9 8 7 6 RE-Submit Characteristics of Linear Relations This booklet belongs to: Period LESSON # DATE QUESTIONS FROM NOTES Questions that I find difficult Pg. Pg. Pg. Pg. Pg. Pg. Pg. Pg. Pg.
MATH 150 Pre-Calculus
MATH 150 Pre-Calculus Fall, 2014, WEEK 5 JoungDong Kim Week 5: 3B, 3C Chapter 3B. Graphs of Equations Draw the graph x+y = 6. Then every point on the graph satisfies the equation x+y = 6. Note. The graph
Connected Mathematics 2, 6 th and 7th Grade Units 2009 Correlated to: Washington Mathematics Standards for Grade 5
Grade 5 5.1. Core Content: Multi-digit division (Operations, Algebra) 5.1.A Represent multi-digit division using place value models and connect the representation to the related equation. 5.1.B Determine
Equations of Lines and Linear Models
8. Equations of Lines and Linear Models Equations of Lines If the slope of a line and a particular point on the line are known, it is possible to find an equation of the line. Suppose that the slope of
MS Algebra A-S-ID-7 Ch. 5.5a Find Slope Given Two Points. ALGEBRA SUPPORT Day 1 of 2 Find Slope and Rate of Change
MS Algebra ASID7 Ch. 5.5a Find Slope Given Two Points ALGEBRA SUPPORT Day 1 of 2 Find Slope and Rate of Change Title: 5.5a Find Slope Given Two Points Day 1 of 2 Date: SUPPORT Class Learning Target By
Foundations of Math II Unit 3: Similarity and Congruence
Foundations of Math II Unit 3: Similarity and Congruence Academics High School Mathematics 3.1 Warm Up 1. Jill and Bill are doing some exercises. Jayne Funda, their instructor, gently implores Touch your
1 Write a Function in
www.ck12.org Chapter 1. Write a Function in Slope-Intercept Form CHAPTER 1 Write a Function in Slope-Intercept Form Here you ll learn how to write the slope-intercept form of linear functions and how to
Use the Point-Slope Form to Write the Equation of a Line
Math 90 8.3 "Writing Equations of Lines" Objectives: * Use the point-slope form to write the equation of a line. * Use the slope-intercept form to write the equation of a line. * Use slope as an aid when
The Slope of a Line. units corresponds to a horizontal change of. m y x y 2 y 1. x 1 x 2. Slope is not defined for vertical lines.
0_0P0.qd //0 : PM Page 0 0 CHAPTER P Preparation for Calculus Section P. (, ) = (, ) = change in change in Figure P. Linear Models and Rates of Change Find the slope of a line passing through two points.
Name: Date: Period: Activity 4.6.2: Point-Slope Form of an Equation. 0, 4 and moving to another point on the line using the slope.
Name: Date: Period: Activity.6.2: Point-Slope Form of an Equation 1.) Graph the equation y x = + starting at ( ) 0, and moving to another point on the line using the slope. 2.) Now, draw another graph
coordinate system: (0, 2), (0, 0), (0, 3).
Lesson. Objectives Find the slope of a line from the graph of the line. Find the slope of a line given two points on the line. Activity The Slope of a Line A surveyor places two stakes, A and B, on the
Lesson 1b Linear Equations
In the first lesson we looked at the concepts and rules of a Function. The first Function that we are going to investigate is the Linear Function. This is a good place to start because with Linear Functions,
2.1 Slope and Parallel Lines
Name Class ate.1 Slope and Parallel Lines Essential Question: How can ou use slope to solve problems involving parallel lines? Eplore Proving the Slope Criteria for Parallel Lines Resource Locker The following
Section 2.3 Task List
Summer 2017 Math 108 Section 2.3 67 Section 2.3 Task List Work through each of the following tasks, carefully filling in the following pages in your notebook. Section 2.3 Function Notation and Applications
Unit 3 Algebra What is the y-intercept for the graph of the equation 3x 5y = 15?
Unit 3 lgebra 1 Name: ate: 1. The equation below is used to find (x, y) coordinates. y = 3x + 2 3. ennie is using this pattern to make stars for an laska state flag. Which coordinates could be found using
Step 2: Extend the compass from the chosen endpoint so that the width of the compass is more than half the distance between the two points.
Student Name: Teacher: Date: District: Miami-Dade County Public Schools Test: 9_12 Mathematics Geometry Exam 1 Description: GEO Topic 1 Test: Tools of Geometry Form: 201 1. A student followed the given
Geometry Unit 3 Note Sheets Date Name of Lesson. Slopes of Lines. Partitioning a Segment. Equations of Lines. Quiz
Date Name of Lesson Slopes of Lines Partitioning a Segment Equations of Lines Quiz Introduction to Parallel and Perpendicular Lines Slopes and Parallel Lines Slopes and Perpendicular Lines Perpendicular
WITH MATH INTERMEDIATE/MIDDLE (IM) GRADE 6
May 06 VIRGINIA MATHEMATICS STANDARDS OF LEARNING CORRELATED TO MOVING WITH MATH INTERMEDIATE/MIDDLE (IM) GRADE 6 NUMBER AND NUMBER SENSE 6.1 The student will identify representations of a given percent
Algebra I Notes Unit Seven: Writing Linear Equations
Sllabus Objective.6 The student will be able to write the equation of a linear function given two points, a point and the slope, table of values, or a graphical representation. Slope-Intercept Form of
Homework 5 - Section 3.3 #5
Homework 5 - Section. #5 Intermediate Algebra / MAT 15 Fall 01 possible master (Prof. Fleischner) Student Name/ID: 1. Rewrite the equation in A + B = C form. Use integers for A, B, and C. + 5 = +. Rewrite
4.5 Equations of Parallel and Perpendicular Lines
Name Class Date.5 Equations of Parallel and Perpendicular Lines Essential Question: How can ou find the equation of a line that is parallel or perpendicular to a given line? Resource Locker Eplore Eploring
Plotting Points in 2-dimensions. Graphing 2 variable equations. Stuff About Lines
Plotting Points in 2-dimensions Graphing 2 variable equations Stuff About Lines Plotting Points in 2-dimensions Plotting Points: 2-dimension Setup of the Cartesian Coordinate System: Draw 2 number lines:
Sect Linear Equations in Two Variables
99 Concept # Sect. - Linear Equations in Two Variables Solutions to Linear Equations in Two Variables In this chapter, we will examine linear equations involving two variables. Such equations have an infinite
8.EE. Development from y = mx to y = mx + b DRAFT EduTron Corporation. Draft for NYSED NTI Use Only
8.EE EduTron Corporation Draft for NYSED NTI Use Only TEACHER S GUIDE 8.EE.6 DERIVING EQUATIONS FOR LINES WITH NON-ZERO Y-INTERCEPTS Development from y = mx to y = mx + b DRAFT 2012.11.29 Teacher s Guide:
Then finding the slope, we can just use the same method that we have done the other ones we get the slope 4 1
169 Graphing Equations with Slope Okay, now that you know how to graph a line by getting some points, and you know how to find the slope between two points, you should be able to find the slope of a line
Economics 101 Summer 2015 Answers to Quiz #1 Thursday, May 28, 2015
Economics 101 Summer 2015 Answers to Quiz #1 Thursday, May 28, 2015 Name Please write your answers neatly and legibly. 1. Zerbia is a country that produces two types of goods: consumer goods and capital
Unit 1 Introduction to Precalculus Linear Equations in Two Variables (Unit 1.3)
Unit 1 Introduction to Precalculus Linear Equations in Two Variables (Unit 1.3) William (Bill) Finch Mathematics Department Denton High School Lesson Goals When ou have completed this lesson ou will: Find