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 of various linear equations and graphs when given two points. I will demonstrate this by completing Four- Square Notes and by solving problems in a pair/group activity. Teacher Note: Graph paper helpful for this lesson.
Home Work 1-2-3: 1) Class 4-Square Notes Put In Binder? 2) Section 5.5 Pg. 286-289 3) Section TxtBk. Prob.#5-17 Odd Notes Copied on blank sheet Solved and Put in Binder? of paper in Binder? Table of Contents Date Description Date Due
Storm Check (Think, Write, Discuss, Report) Questions on which to ponder and answer: 1. How are the two images similar? 2. How are they different? 3. How can these two images be related to math?
Daily Warm-Up Exercises For use with pages xxx xxx A cross-country skier traveled 14 miles in 3.5 hours. Use the formula d = r t where d is distance, r is rate, and t is time, to find the average rate of speed.
Daily Warm-Up Exercises For use with pages xxx xxx A cross-country skier traveled 14 miles in 3.5 hours. Use the formula d = r t where d is distance, r is rate, and t is time, to find the average rate of speed. ANSWER 4 mi/h
Vocabulary Rate of Change 1) Slope 2) Rise 3) Run 4) Slope-Intercept Form 5) Point-Slope Form
Sketch DAY 2 1. Review word Friendly Definition Physical Representation 2. Draw a sketch Wordwork 1. 2. 3. 4. DAY 3 and/or DAY 4 1. Review the word Friendly Definition Physical Representation 2. Show how the word works Synonyms/antonym Word Problems Related words/phrases Example/non-example Word List Friendly Definition DAY 1 1. Use Visuals 2. Introduce the word Friendly Definition Physical Representation 3. Use Cognates 4. Write friendly definition 5. Physical Representation DAY 5 1. Review the word Friendly definition Physical Representation Sentence 3. Write a sentence at least 2 rich words (1 action) correct spelling correct punctuation correct subject/predicate agreement clear and clean writing
Notes: Types of SLOPES of a Linear Equation y = mx + b Positive m = slope = rise/run = change in y / change in x b = y-intercept = where graph crosses y-axis x = independent variable, y = dependent variable Negative + m - m Zero Undefined m = 0 (horizontal) m =??(vertical) Dividing by Zero
Problem A Find a slope of a VERTICAL line STEP 1) You need two (2) points to find the slope: (3, 5) and (3, 1) STEP 2) Make a table of points x y STEP 3) - denominator = = - numerator STEP 4) Make a fraction with the values from STEP 3. m=
Problem A Find a slope of a VERTICAL line STEP 1) You need two (2) points to find the slope: (3, 5) and (3, 1) STEP 2) Make a table of points STEP 3) 3-3 denominator x y 3 5 3 1 5-1 = 0 = 4 numerator STEP 4) Make a fraction with the values from STEP 3. m= 4 0 =?? Division by zero is undefined.
Problem B Find a slope of a HORIZONTAL line STEP 1) You need two (2) points to find the slope: (-2, 4) and (4, 4) STEP 2) Make a table of points x y STEP 3) - denominator = = - numerator STEP 4) Make a fraction with the values from STEP 3. m=
Problem B Find a slope of a HORIZONTAL line STEP 1) You need two (2) points to find the slope: (-2, 4) and (4, 4) STEP 2) Make a table of points x y 4 4 STEP 3) 4 -(-2) denominator -2 4 4-4 = 6 = 0 numerator STEP 4) Make a fraction with the values from STEP 3. m= 0 6 = 0
Storm Check (Think, Write, Discuss, Report) What are the four types of slope? The four types of slope are: 1) 2) 3) 4)
Storm Check (Think, Write, Discuss, Report) What are the four types of slope? The four types of slope are: 1) Positive 2) Negative 3) Zero (horizontal) 4) Undefined (vertical)
Title: 5.5a Find Slope Given Two Points Date: Learning Target By the end of the period, I will find the slope of various linear equations and graphs when given two points. I will demonstrate this by completing Four- Square Notes and by solving problems in a pair/group activity. Teacher Note: Graph paper helpful for this lesson.
Home Work 1-2-3: 1) Class 4-Square Notes Put In Binder? 2) Section 5.5 Pg. 286-289 3) Section TxtBk. Prob.#6-18 Even Notes Copied on blank sheet Solved and Put in Binder? of paper in Binder? Table of Contents Date Description Date Due
Notes: Finding SLOPE of a Linear Equation y = mx + b m = slope = rise/run = change in y / change in x b = y-intercept = where graph crosses y-axis x = independent variable, y = dependent variable STEP 1) You need two (2) points to find the slope: (x 1, y 1 ) and (x 2, y 2 ) STEP 2) Make a table of points x y x 2 y 2 STEP 3) x 2 - x 1 x 1 y 1 y 2 - y 1 STEP 4) Make a fraction with the values from STEP 3. m = y 2 y 1 x 2 x 1 denominator numerator
Example: Finding SLOPE of a Linear Equation y = mx + b m = slope = rise/run = change in y / change in x b = y-intercept = where graph crosses y-axis x = independent variable, y = dependent variable STEP 1) You need two (2) points to find the slope: (1, 2) and (2, 5) STEP 2) Make a table of points STEP 3) 2-1 denominator x y 2 5 1 2 5-2 = 1 = 3 numerator STEP 4) Make a fraction with the values from STEP 3. m = 3 1
Problem A Find a positive slope STEP 1) You need two (2) points to find the slope: (-4, 2) and (2, 6) STEP 2) Make a table of points x y STEP 3) - denominator = = - numerator STEP 4) Make a fraction with the values from STEP 3. m = =
Problem A Find a positive slope STEP 1) You need two (2) points to find the slope: (-4, 2) and (2, 6) STEP 2) Make a table of points x y 2 6 STEP 3) 2 -(-4) denominator -4 2 6-2 = 6 = 4 numerator STEP 4) Make a fraction with the values from STEP 3. m = 4 = 2 6 3
Problem B Find a negative slope STEP 1) You need two (2) points to find the slope: (3, 5) and (6, -1) STEP 2) Make a table of points x y STEP 3) - denominator = = - numerator STEP 4) Make a fraction with the values from STEP 3. m =
Problem B Find a negative slope STEP 1) You need two (2) points to find the slope: (3, 5) and (6, -1) STEP 2) Make a table of points STEP 3) 6-3 denominator x y 6-1 3 5-1 - 5 = 3 = -6 numerator STEP 4) Make a fraction with the values from STEP 3. m= -6 3 =-2
Storm Check (Think, Write, Discuss, Report) How do you find the slope for a given linear equation? (3 or 4 sentences) To find the slope for a given linear equation, I have to.
Guided Practice slope of the line that passes through the points. (0, 6) and (5, - 4) (5, 2) and (4, -1) x y x y
Guided Practice slope of the line that passes through the points. (0, 6) and (5, - 4) (5, 2) and (4, -1) x y x y 5-4 4-1 5 0 0 6-4 6 4 5 5 2-1 2 =5 = -10 5 ANSWER = -2 =-10 = -1 = -3-1 ANSWER = 3 = -3
Vocabulary Rate of Change 1) Slope 2) Rise 3) Run 4) Slope-Intercept Form 5) Point-Slope Form
Sketch DAY 2 1. Review word Friendly Definition Physical Representation 2. Draw a sketch Wordwork 1. 2. 3. 4. DAY 3 and/or DAY 4 1. Review the word Friendly Definition Physical Representation 2. Show how the word works Synonyms/antonym Word Problems Related words/phrases Example/non-example Word List Friendly Definition DAY 1 1. Use Visuals 2. Introduce the word Friendly Definition Physical Representation 3. Use Cognates 4. Write friendly definition 5. Physical Representation DAY 5 1. Review the word Friendly definition Physical Representation Sentence 3. Write a sentence at least 2 rich words (1 action) correct spelling correct punctuation correct subject/predicate agreement clear and clean writing
Title: 5.5a Find Slope Given Two Points Date: Learning Target By the end of the period, I will find the slope of various linear equations and graphs when given two points. I will demonstrate this by completing Four- Square Notes and by solving problems in a pair/group activity. Teacher Note: Graph paper helpful for this lesson.
Home Work 1-2-3: 1) Class 4-Square Notes Put In Binder? 2) Section 5.5 Pg. 286-289 3) Section TxtBk. Prob.#5-18 ALL Notes Copied on blank sheet Solved and Put in Binder? of paper in Binder? Table of Contents Date Description Date Due
Graph the function ( y = mx + b ) Ticket OUT. 2x 5y = 10 Step 1) Step 2) Step 3) Solve for y Plot y-intercept Plot the slope 2 or 3 times x y
Graph the function ( y = mx + b ) Step 1) m = 2 5 Step 2) Step 3) 2x 5y = 10 2x 5y = 10-2x = -2x -5y = -2x +10-5 -5-5 x y = 2x -2 5 b = -2 (0, -2) y -5-4 5 0 (-5, -4) (0, -2) Step 1) Step 2) Step 3) Ticket OUT. ANSWER Solve for y Plot y-intercept Plot the slope 2 or 3 times (5, 0)