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**Objective: To graph linear equations**

Ch 4.2 Objective: To graph linear equations

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**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.

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**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.

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**Comparison One Variable Equations Two Variable Equations x + y = 5**

Ordered Pairs (x,y) x y Solutions: 1 2 4 5 7 4 3 1 -2 x = 1, y = 4 (1,4) 2x = 14 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

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**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) = 5 Yes Yes 3(-1) - 2 = 5 No

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**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

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**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

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**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

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**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

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**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

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**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.

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**Solve the following equations for y. (Function Form)**

1) 2x + y = 5 2) -x + 2y = -4 -2x x +x x 2y = x - 4 y = -2x + 5

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**Rewrite the equation in function form.**

3) 3x + 5y = 10 4) -2x + 3y = -6 -3x x +2x x 5y = -3x + 10 3y = 2x - 6

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**Solve the equation for y, complete the chart, and graph.**

1) 3x + 2y = 4 -3x x y x y 2y = -3x + 4 -4 -2 2 4 6 8 5 2 x -1 -4 -7

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**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 -2 x -1 1

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**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 5 4 x 3 2 1

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