1. 2-3-11 Please have hw out to correct.

2. Equations with Two Variables Lesson 8-2 p.391

3. Equations with Two Variables In the other chapters, we learned how to solve equations like this: 5x + 3 = 2x +9 In this type of equation, there was only one kind of variable—”x”. Now we will learn how to solve variables like: y = 2x + 3

4. Equations with Two Variables y = 2x + 3 What do you notice about this equation?

5. Equations with Two Variables y = 2x + 3 What do you notice about this equation? Yes there are two kinds of variables—an x and a y. We will find in this chapter that the solution to this type of equation is an ordered pair and if we graph the ordered pairs of the equation, we get a straight line when the points are connected.

6. Equations with Two Variables We will also find that an equation like y = 2x + 3 can have many solutions, not just one, but it is the graph of the solutions that will be our answer. Let’s start with one way to solve this type of problem...a t-table or t-chart

7. Equations with Two Variables y = 2x + 3 One strategy is to make a table of values or a t-table. It looks like this: XY

8. Equations with Two Variables y = 2x + 3 We begin by choosing any value we want for x. This may seem odd to you, but the reason will become apparent later. I like to choose one positive number, one negative number and the number zero.

9. Equations with Two Variables y = 2x + 3 Let’s choose 1, 0 and -2 xy 1Place the x values in 0the chart. This reminds -2us which numbers to substitute for x.

10. Equations with Two Variables y = 2x + 3Then we substitute each value one at a time and x ysolve for “y” 1 52(1) + 3 = 5 0 -2

11. Equations with Two Variables y = 2x + 3Then we substitute each value one at a time and x ysolve for “y” 1 52(1) + 3 = 5 0 32(0) + 3 = 3 -2

12. Equations with Two Variables y = 2x + 3Then we substitute each value one at a time and x ysolve for “y” 1 52(1) + 3 = 5 0 32(0) + 3 = 3 -2 -12(-2) + 3 = -1

13. Equations with Two Variables The information in the t-table is a series of ordered pairs that when graphed on the coordinate plane, will result in a straight line like this

14. Equations with Two Variables x y 1 5 0 3 -2 -1 First, plot point (1,5)

15. Equations with Two Variables x y 1 5 0 3 -2 -1 First, plot point (1,5)

16. Equations with Two Variables x y 1 5 0 3 -2 -1 First, plot point (1,5) Then plot point (0,3)

17. Equations with Two Variables x y 1 5 0 3 -2 -1 First, plot point (1,5) Then plot point (0,3)

18. Equations with Two Variables x y 1 5 0 3 -2 -1 First, plot point (1,5) Then plot point (0,3) Then plot point (-2,-1)

19. Equations with Two Variables x y 1 5 0 3 -2 -1 First, plot point (1,5) Then plot point (0,3) Then plot point (-2,-1) Finally draw a line that connects and goes through the points.

20. Equations with Two Variables This is the graph of the equation: y = 2x + 3 We will find that each equation has its own unique graph.

21. Try This Make a t-table for the equation y = 3x -2 using the following values for x xy 3 0

22. Try This Make a t-table for the equation y = 3x -2 using the following values for x xy 373(3) – 2 = 7 0

23. Try This Make a t-table for the equation y = 3x -2 using the following values for x xy 373(3) – 2 = 7 0 -23(0) – 2 = -2

24. Try This Make a t-table for the equation y = 3x -2 using the following values for x xy 373(3) – 2 = 7 0 -23(0) – 2 = -2 -1 -53(-1) – 2 = -5

25. Try This xy 37 0 -2 -1 -5 Now graph the Ordered pairs

26. Try This xy 37 0 -2 -1 -5

27. One more Thing Sometimes, an equation will be given as well as a sample ordered pair, and you will be asked “Is this a solution to the equation?” For example, is (4,3) a solution to this equation: y = -2x + 2 Substitute the ordered pair in the solution: 3 = -2(4) + 2 In this case 3 = -8 + 2 or 3 = -6 is not true, so no it is not a solution.

28. Try This Is (3,0) a solution to y = 2x – 6 0 = 6 – 6 0=0 Is (-2,5) a solution to y = -3x + 1 5 = 7

29. Try This Is (3,0) a solution to y = 2x – 6 yes Is (-2,5) a solution to y = -3x + 1 no

30. 2-3-11 Agenda PA#13: Pp.394-395 #12-18 even, 20-30 even