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

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.

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

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

Graphing by Solving for y x y=½ x + 3 (x,y) -2 ½(-2) +3= -1 + 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

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

Graphing by Solving for y x 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

Graphing by Solving for y x 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)

Graphing by Solving for y x y=3/2x+3 (x,y) -2 3/2(-2)+3 = -3+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

Homework: Pages 408-409, #s 21-26, 36, 38, 39 See handout sheet