1. Copyright © 2010 Pearson Education, Inc. All rights reserved. 3.4 – Slide 1

2. Copyright © 2010 Pearson Education, Inc. All rights reserved. 3.4 – Slide 2 Graphs of Linear Equations and Inequalities; Functions Chapter 3

3. Copyright © 2010 Pearson Education, Inc. All rights reserved. 3.4 – Slide 3 3.4 Equations of Lines

4. Copyright © 2010 Pearson Education, Inc. All rights reserved. 3.4 – Slide 4 3.4 Equations of Lines Objectives 1.Write an equation of a line given its slope and y- intercept. 2.Graph a line given its slope and a point on the line. 3.Write an equation of a line given its slope and any point on the line. 4.Write an equation of a line given two points on the line. 5.Write an equation of a line parallel or perpendicular to a given line. 6.Write an equation of a line that models real data.

5. Copyright © 2010 Pearson Education, Inc. All rights reserved. 3.4 – Slide 5 Write an equation of a line given slope and y-intercept. 3.4 Equations of Lines

6. Copyright © 2010 Pearson Education, Inc. All rights reserved. 3.4 – Slide 6 3.4 Equations of Lines Example 1 Write an equation of the line with slope 2/3 and y- intercept (0,  1). Write an equation of a line given slope and y-intercept.

7. Copyright © 2010 Pearson Education, Inc. All rights reserved. 3.4 – Slide 7 3.4 Equations of Lines Graph a line given its slope and a point on the line.

8. Copyright © 2010 Pearson Education, Inc. All rights reserved. 3.4 – Slide 8 3.4 Equations of Lines Example 2 Graph 2x – 3y = 3 by using the slope and y-intercept. (continued) Graph a line given its slope and a point on the line.

9. Copyright © 2010 Pearson Education, Inc. All rights reserved. 3.4 – Slide 9 3.4 Equations of Lines Example 2 Graph 2x – 3y = 3 by using the slope and y-intercept. (continued) Graph a line given its slope and a point on the line.

10. Copyright © 2010 Pearson Education, Inc. All rights reserved. 3.4 – Slide 10 3.4 Equations of Lines Example 2 Graph 2x – 3y = 3 by using the slope and y-intercept. Graph a line given its slope and a point on the line.

11. Copyright © 2010 Pearson Education, Inc. All rights reserved. 3.4 – Slide 11 3.4 Equations of Lines Example 4 Write an equation, in slope-intercept form, of the line having slope 4 passing through (2, 5). Write an equation of a line given its slope and any point on the line. Substitute x = 2, y = 5 and the given slope m = 4 into y = mx + b and solve for b.

12. Copyright © 2010 Pearson Education, Inc. All rights reserved. 3.4 – Slide 12 3.4 Equations of Lines Write an equation of a line given its slope and any point on the line.

13. Copyright © 2010 Pearson Education, Inc. All rights reserved. 3.4 – Slide 13 3.4 Equations of Lines Example 5b Write an equation of the line through (4, 2), with slope 3/5. Give the final answer in slope-intercept form. Write an equation of a line given its slope and any point on the line.

14. Copyright © 2010 Pearson Education, Inc. All rights reserved. 3.4 – Slide 14 3.4 Equations of Lines Example 6 Write an equation of the line through the points (  2, 5) and (3, 4). Give the final answer in slope-intercept form. Write an equation of a line given two points on the line. Now use either point and the point-slope form. Using (3, 4) gives (continued)

15. Copyright © 2010 Pearson Education, Inc. All rights reserved. 3.4 – Slide 15 3.4 Equations of Lines Example 6 Write an equation of the line through the points (  2, 5) and (3, 4). Give the final answer in slope-intercept form. Write an equation of a line given two points on the line.

16. Copyright © 2010 Pearson Education, Inc. All rights reserved. 3.4 – Slide 16 3.4 Equations of Lines Write an equation of a line given two points on the line. Ax + By = C, called standard form, where A, B, and C are real numbers and A and B are not both 0. In most cases, A, B, and C are rational numbers.

17. Copyright © 2010 Pearson Education, Inc. All rights reserved. 3.4 – Slide 17 3.4 Equations of Lines Example 7a Find the equation in slope-intercept form passing through the point (  4, 5) and (a) parallel to the line 2x + 3y = 6; (b) perpendicular to the line 2x + 3y = 6. Write an equation of a line parallel or perpendicular to a given line. Find the slope of the line 2x + 3y = 6. (continued)

18. Copyright © 2010 Pearson Education, Inc. All rights reserved. 3.4 – Slide 18 3.4 Equations of Lines Example 7a Find the equation in slope-intercept form passing through the point (  4, 5) and parallel to the line 2x + 3y = 6 Write an equation of a line parallel or perpendicular to a given line. Parallel lines have the same slope. Use the point-slope form. (continued)

19. Copyright © 2010 Pearson Education, Inc. All rights reserved. 3.4 – Slide 19 3.4 Equations of Lines Example 7a Find the equation in slope-intercept form passing through the point (  4, 5) and parallel to the line 2x + 3y = 6 Write an equation of a line parallel or perpendicular to a given line.

20. Copyright © 2010 Pearson Education, Inc. All rights reserved. 3.4 – Slide 20 3.4 Equations of Lines Example 7b Find the equation in slope-intercept form passing through the point (  4, 5) and perpendicular to the line 2x + 3y = 6. Write an equation of a line parallel or perpendicular to a given line. The slope of the line is –2/3. A line that is perpendicular must have a slope that is the negative reciprocal or 3/2.

21. Copyright © 2010 Pearson Education, Inc. All rights reserved. 3.4 – Slide 21 3.4 Equations of Lines

22. Copyright © 2010 Pearson Education, Inc. All rights reserved. 3.4 – Slide 22 3.4 Equations of Lines

23. Copyright © 2010 Pearson Education, Inc. All rights reserved. 3.4 – Slide 23 3.4 Equations of Lines Example 8a It is time to fill your car with gasoline. Gas is selling for $4.50 per gallon. Write an equation that describes the cost y to buy x gallons of gas. Write an equation of a line that models real data.

24. Copyright © 2010 Pearson Education, Inc. All rights reserved. 3.4 – Slide 24 3.4 Equations of Lines Example 8b You can also get a car wash at the gas station if you pay an additional $3.00. Write an equation that defines the price for gas and a car wash. Write an equation of a line that models real data. Since an additional $3.00 will be charged, you pay $4.50x + 3.00 dollars for x gallons of gas and a car wash.

25. Copyright © 2010 Pearson Education, Inc. All rights reserved. 3.4 – Slide 25 3.4 Equations of Lines Example 8c Interpret the ordered pairs (5, 25.5) and (10, 48) in relation to the equation from part b. Write an equation of a line that models real data. The ordered pair (5, 25.5) indicates that the price of 5 gal of gas and a car wash is $25.50. Similarly, (10, 48) indicates that the price of 10 gal of gas and a car wash is $48.00.