1. Equations With Two Variables pages 405 - 409
Section 8.2 part 2
Equations With Two Variables
pages

2. In the last lesson we:
Found solutions of two-variable equations by replacing a variable with a value then solving the equation for a solution. Solutions of two-variable equations are written as ordered pairs.
Graphed two-variable equations by making a table of values to show ordered pair solutions, graphed the ordered pairs, then drew a line through the points.

3. Graphing y = a and x = b y = 2 For every value of x, y = 2. x = 2
For every value of y, x = 2. y y x x x x

4. Graphing by Solving for y
Sometimes an equation will have to be solved for y before it can be graphed.
Solve y - ½ x = 3 for y. Then graph the equation.
y - ½ x = 3
+ ½ x = + ½ x
y = ½ x + 3

5. Graphing by Solving for yx
y=½ x + 3
(x,y) -2
½(-2) +3= = 2
(-2, 2)
½(0) + 3=
0 + 3 = 3
(0,3) 2
½(2) + 3=
1 + 3 = 4
(2,4)
y = ½ x + 3

6. Check Understanding
Solve each equation for y Then graph the equation.
2x + y = 3
y – x = 5
-3x + 2y = 6

7. Graphing by Solving for yx
y = -2x+3
(x,y) -1
-2(-1)+3 = 2+3=5
(-1,5)
-2(0)+3 = 0+3=3
(0,3) 1
-2(1)+3 = -2+3=1
(1,1)
y = -2x + 3

8. Graphing by Solving for yx
y = x + 5
(x,y) -2
-2+5=3
(-2,3)
0+5=5
(0,5) 1
1+5=6
(1,6)
y = x + 5 -1
-1+5=4
(-1,4) -3
-3+5=2
(-3,2) -4
-4+5=1
(-4,1)

9. Graphing by Solving for yx
y=3/2x+3
(x,y) -2
3/2(-2)+3 = =0
(-2,0)
3/2(0)+3 = 0+3=3
(0,3) 2
3/2(2)+3 = 3+3=6
(2,6)
y = 3/2x+3

10. Homework:
Pages , #s 21-26, 36, 38, 39
See handout sheet