Chapter 2: Linear Equations/Inequalities of two variables

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1 Chapter 2: Linear Equations/Inequalities of two variables I. Introduction to the Rectangular (Cartesian) Coordinate System II. Linear Equations in 2-variables III. Graphing Using Intercepts IV. Two Special Lines V. Slope VI. Slope-intercept Form VII. Point-Slope Form VIII. Finding Equations of Lines IX. Inequalities of two-variables 1

2 VII. Point-Slope Form Recall: Given the points and on a line, then slope = m = Consider the case where we have a line with given slope m and through. Then for any other point line must satisfy on the (point-slope form) 2

3 y 1) What is the slope of the line? 2) What point lies on the line? x 4) Write in slope-intercept form. 3

4 y 1) What is the slope of the line? 2) What point lies on the line? x 4

5 Identify the slope and a point on each of the given lines. 5

6 Word Problems. Find the linear equation that describes each word problem. Look for a rate (slope) and one point and use Point-Slope form of the line. 1) Arnie was driving at a constant speed of 60mi/hr when he crossed the Sandy river. After 1 hour, he passed a highway marker for mile 84. Write an equation in Point-Slope form THEN find which highway marker he will pass 90 minutes after crossing the Sandy river. 2) A basement filled with water from a rainstorm is drained at a rate of 10.5 liters per minute. After 40 minutes, there are 840 liters of water remaining. Write the equation of a line in Point-Slope form THEN find how long it takes to drain the basement of water. 6

7 VIII. Finding Equations of Lines Finding Equations When finding equations of a line, we utilize the forms Note that we need the slope in order to use either of Find the equation of the line. Write your final answer in slopeintercept form. 1) Has a slope of 6/5 and y-intercept of (0, -8). 2) Has a slope of -4 and y-intercept of (0, 5). 7

8 3) Slope is -2/3 and y-intercept is (6,3). 4) Contains the points (3,-3) and (9,7). 5) Slope 5 and contains the point (2, 9). 6) Contains the points (7, -2) and (-7, -6). 8

9 7) Has the graph shown. y (0, 6) (-4, 0) x 9

10 8) Has the graph shown. X Y y x

11 Word problems. Write an linear equation that describes the following word problems. Look for two data points and then use either Point- Slope or Slope-intercept form of the line. 1). In 1990, about 13.8 million students were enrolled in U.S. colleges. In 2000, about 14.9 million students were projected to be enrolled in U.S. colleges. Find a linear equation that fits this data. Define your variables. 11

12 Word problems. Write an linear equation that describes the following word problems. Look for two data points and then use either Point- Slope or Slope-intercept form of the line. 2) In 1995, a public library had 16,000 books on its shelves. In 1999, the library had 19,000 books. Find a linear equation that describes this trend. How many books are on the shelves in 2004 if this trend continues? 12

13 Word problems. Write an linear equation that describes the following word problems. Look for two data points and then use either Point- Slope or Slope-intercept form of the line. 3) You buy a new car and it costs $21,000. Five years later, it is only worth $13,500. If this trend of depreciation continues, when will the car become worthless? 13

14 Chapter 2 Homework Part VII: Point-Slope Form 27) What is the slope of the line 28) Give a point that lies on the line 29) What is the slope of the line 14

15 Part VIII: Finding the Equation of Lines 30) Find the equation of the line that has slope of and a y-intercept of 31) Find the equation of the line that passes through the points (0,4) and (-2,-5). 32) Find the equation of the line with slope of 7 and contains the point (5,8). 33) Find the equation of the line through the points (7,2) and (7,5). 34) Find the equation of the line passing through the points (-3,4) and (-3,8). 15

16 16

Lesson 11: Linear Functions, Part 2

Lesson 11: Linear Functions, Part 2 Lesson 11 continues the study of linear functions. In this lesson, we look at how to write linear equations in slope-intercept and general form and applications where these may be used. We also look at