Objective: To graph linear equations Ch 4.2 Objective: To graph linear equations

Definitions Linear Equation An equation containing two variables that when points are plotted create a line. Generally of the form: ax + by = c where (x,y) are coordinates and a, b, and c are numbers.

Steps for graphing Choose a value for “x”. Plug that value into the equation and solve for “y”. Plot the coordinate (x,y). Choose another value for “x” Plug that value into the equation and solve for “y” Draw a line through the two points.

Comparison One Variable Equations Two Variable Equations x + y = 5 Ordered Pairs (x,y) x y +3 +3 Solutions: 1 2 4 5 7 4 3 1 -2 x = 1, y = 4 (1,4) 2x = 14 2 2 x = 2, y = 3 (2,3) x = 7 x = 4, y = 1 (4,1) x = 5, y = 0 (5,0) One Solution x = 7, y = -2 (7,-2) Infinite Solutions

State whether the given point is a solution to 3x - y = 5. 1) (2, 1) 2) (4, 5) 3) (-3, -14) 4) 5) (-1, 2) 3(2) - 1 = 5 Yes 3(4) - 5 = 5 No 3(-3) - -14 = 5 Yes Yes 3(-1) - 2 = 5 No

Complete the chart and graph. y y = 2x - 3 x y -3 -2 -1 1 2 3 2(-3) - 3 = -9 2(-2) - 3 = -7 -5 x -3 -1 1 3

Complete the chart and graph. y y = 2x - 3 x y -3 -2 -1 1 2 3 2(-3) - 3 = -9 2(-2) - 3 = -7 -5 x -3 -1 1 3

Complete the chart and graph. y y = 2x - 3 x y -3 -2 -1 1 2 3 2(-3) - 3 = -9 2(-2) - 3 = -7 -5 x -3 -1 1 3

Complete the chart and graph. y y = 2x - 3 x y -3 -2 -1 1 2 3 2(-3) - 3 = -9 2(-2) - 3 = -7 -5 x -3 -1 1 3

Complete the chart and graph. y y = 2x - 3 x y -3 -2 -1 1 2 3 2(-3) - 3 = -9 2(-2) - 3 = -7 -5 x -3 -1 1 3

Complete the chart and graph. y y = 2x - 3 x y -3 -2 -1 1 2 3 2(-3) - 3 = -9 2(-2) - 3 = -7 -5 x -3 -1 1 3 This line represents all real solutions to y = 2x - 3.

Solve the following equations for y. (Function Form) 1) 2x + y = 5 2) -x + 2y = -4 -2x -2x +x +x 2y = x - 4 y = -2x + 5 2 2

Rewrite the equation in function form. 3) 3x + 5y = 10 4) -2x + 3y = -6 -3x -3x +2x +2x 5y = -3x + 10 3y = 2x - 6 5 5 3 3

Solve the equation for y, complete the chart, and graph. 1) 3x + 2y = 4 -3x -3x y x y 2y = -3x + 4 -4 -2 2 4 6 8 2 2 5 2 x -1 -4 -7

Rewrite in function form, complete the chart, and graph. 2) x - 3y = 6 -x -x y x y -3y = -x + 6 -6 -3 3 6 9 -4 -3 -3 -3 -2 x -1 1

Solve the equation for y, find at least five solutions, and graph. 3) x + 2y = 8 y -x -x x y 2y = -x + 8 -4 -2 2 4 6 6 2 2 5 4 x 3 2 1