1. Warm-Up 1) Determine whether the point (0,3) is a solution to y = 5x + 3. 5 minutes 2) Graph y = -2x + 1

2. 7.3.1 Linear Equations and Their Graphs 7.3.1 Linear Equations and Their Graphs Objectives: To graph linear equations in two variables

3. Linear Equations y = 3x + 76y = -2 9x – 15y = 7 Linear Equations Equations whose graphs are lines are linear equations. Here are some examples: Nonlinear Equations y = x 2 - 4x 2 + y 2 = 16 xy = 3

4. Example 1 Graph the equation 2x + 2y = 6. 2x + 2y = 6 xy 3 2 5 0 1 -2 2x + 2y = 6solve for y -2x 2y = 6 – 2x 22 y = 3 - x y = 3 - (0)= 3 y = 3 - (1)= 2 y = 3 - (-2)= 5

5. Example 1 Graph the equation 2x + 2y = 6. 2x + 2y = 6 xy 3 2 5 0 1 -2 -8-6-4 -2 2 42 68 4 6 -4 -6 -8 -2 8

6. Practice Graph these linear equations using three points. 1) 3y – 12 = 9x 2) 4y + 8 = -16x

7. Example 2 Graph the equation 3y – 6 = 9x. 3y – 6 = 9x xy 2 5 -4 0 1 -2 3y – 6 = 9xsolve for y +6 3y = 9x + 6 33 y = 3x + 2 y = 3(0) + 2= 2 y = 3(1) + 2= 5 y = 3(-2) + 2= -4

8. Example 2 Graph the equation 3y – 6 = 9x. 3y – 6 = 9x xy 2 5 -4 0 1 -2 -8-6-4 -2 2 42 68 4 6 -4 -6 -8 -2 8

9. Practice Graph these linear equations using three points. 1) 6x – 2y = -2 2) -10x – 2y = 8

10. Homework p.316 #1,3,7,11,15 *Use graph paper for the homework

11. Warm-Up 6 minutes 1) Graph 4x – 3y = 12 * Get 2 sheets of graph paper and a ruler

12. 7.3.2 Linear Equations and Their Graphs 7.3.2 Linear Equations and Their Graphs Objectives: To graph linear equations using intercepts

13. Graphing Using Intercepts The x-intercept of a line is the x-coordinate of the point where the line intercepts the x-axis. -8-6-4 -2 2 42 68 4 6 -4 -6 -8 -2 8 The line shown intercepts the x-axis at (2,0). We say that the x-intercept is 2.

14. Graphing Using Intercepts The y-intercept of a line is the y-coordinate of the point where the line intercepts the y-axis. -8-6-4 -2 2 42 68 4 6 -4 -6 -8 -2 8 The line shown intercepts the y-axis at (0,-6). We say that the y-intercept is -6.

15. Example 1 Graph 4x – 3y = 12 using intercepts. xy -4 0 4x – 3y = 12 *To find the y-intercept, let x = 0. 4(0) – 3y = 12 0 – 3y = 12 -3y = 12 -3 y = -4

16. Example 1 Graph 4x – 3y = 12 using intercepts. xy -4 0 0 3 4x – 3y = 12 *To find the x-intercept, let y = 0. 4x – 3(0) = 12 4x - 0 = 12 4x = 12 44 x = 3

17. Example 1 -8-6-4 -2 2 42 68 4 6 -4 -6 -8 -2 8 Graph 4x – 3y = 12 using intercepts. xy -4 0 0 3

18. Example 2 Graph 2x + 5y = 10 using intercepts. xy 2 0 2x + 5y = 10 *To find the y-intercept, let x = 0. 2(0) + 5y = 10 0 + 5y = 10 5y = 10 55 y = 2

19. Example 2 Graph 2x + 5y = 10 using intercepts. xy 2 0 0 5 2x + 5y = 10 *To find the x-intercept, let y = 0. 2x + 5(0) = 10 2x + 0 = 10 2x = 10 22 x = 5

20. Example 2 -8-6-4 -2 2 42 68 4 6 -4 -6 -8 -2 8 Graph 2x + 5y = 10 using intercepts. xy 2 0 0 5

21. Practice Graph using intercepts. 1) 5x + 7y = 35 2) 8x + 2y = 24 3) 2y = 3x - 6

22. Homework p.316 #17,20,21,23,26,27 *Use graph paper for the homework

23. Warm-Up 10 minutes Graph these equations: 1)-x + 2y = 4 2) 2x + 3y = 8 3)2x – 1 = y 4)3x – 4y = -12

24. 7.3.3 Linear Equations and Their Graphs 7.3.3 Linear Equations and Their Graphs Objectives: To graph linear equations that graph as horizontal and vertical lines

25. Graphing Horizontal and Vertical Lines The standard form of a linear equation in two variables is Ax + By = C, where A,B, and C are constants and A and B are not both 0. 3x + 4y = 126x + 7y = 23

26. Example 1 -8-6-4 -2 2 42 68 4 6 -4 -6 -8 -2 8 Graph y = -2. write the equation in standard form Ax + By = C (0)x + (1)y = -2 for any value of x y = -2

27. Example 2 -8-6-4 -2 2 42 68 4 6 -4 -6 -8 -2 8 Graph x = 7. write the equation in standard form Ax + By = C (1)x + (0)y = 7 x = 7 for any value of y

28. Practice Graph these equations. 1) x = 5 2) y = -4 3) x = 0

29. Homework p.316 #11,13,19,25,27,35,37,41 *Use graph paper for the homework