Now that you’re practiced with polygons on the grid, let’s take a look at lines.

Graphic designers use lines to create the illusion of curves on the computer screen. Below are some graphic designs created by a graphic designer.  Your mission is to try to duplicate them using what you know about how lines are graphed on the coordinate plane. Use the Cool Math online calculator or your own graphing calculator to graph the designs made with linear equations. List the equations you used to create your design and check them when finished.

Instructions for the Cool Math online calculator Using linear equations create the following graphs in your graphing calculator or with the online graphing tool. Linear Graphing Help

Hint: equations of lines that might be helpful

Slope-Intercept    y = mx + b

Point-Slope      y - y1 = m(x - x1 )

1. 2. List the equations that a designer would have used to create this graph.

Interactive button. Assistance may be required.

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y = − 3 over 2 3 2 x

Interactive button. Assistance may be required.

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y = 3 over 2 3 2 x

Interactive button. Assistance may be required.

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y = -3x

Interactive button. Assistance may be required.

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y = 3x

Interactive button. Assistance may be required.

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y = -x

Interactive button. Assistance may be required.

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y = x

3. List the equations that create a graph.

Interactive button. Assistance may be required.

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y = − 3 over 4 3 4 x − 3

Interactive button. Assistance may be required.

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y = 4 over 3 4 3 x − 4

Interactive button. Assistance may be required.

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y = − 3 over 4 3 4 x + 4

Interactive button. Assistance may be required.

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y = 4 over 3 4 3 x + 3

Interactive button. Assistance may be required.

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y = − 3 over 4 3 4 x + 3

Interactive button. Assistance may be required.

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y = − 3 over 4 3 4 x − 4

4. 5. List the equations that create your graph.

Interactive button. Assistance may be required.

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-6x + y = -16 or y = 6x − 16

Interactive button. Assistance may be required.

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5x − 2y = 16 or y = 5 over 2 5 2 x − 8

Interactive button. Assistance may be required.

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4x − 3y = 14 or y = 4 over 3 4 3 x 14 over 3 14 3

Interactive button. Assistance may be required.

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-3x + 4y = -10 or y = 3 over 4 3 4 x 5 over 2 5 2

Interactive button. Assistance may be required.

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-2x + 5y = -4 or y = 2 over 5 2 5 x 4 over 5 4 5

Interactive button. Assistance may be required.

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x − 6y = 4 or y = 1 over 6 1 6 x + 2 over 3 2 3

6. Challenge Problem
7. List the equations that create your graph.

Interactive button. Assistance may be required.

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4x + 5y = 20

Interactive button. Assistance may be required.

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x + y = 4

Interactive button. Assistance may be required.

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4x+ 11y = 44

Interactive button. Assistance may be required.

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2x + 5y = 20

Interactive button. Assistance may be required.

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4x + 9y = 36

Interactive button. Assistance may be required.

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x + 2y = 8

Interactive button. Assistance may be required.

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4x + 7y = 28

Interactive button. Assistance may be required.

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2x + 3y = 12

Interactive button. Assistance may be required.

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4x- 7y = -28

Interactive button. Assistance may be required.

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x - 2y = -8

Interactive button. Assistance may be required.

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-4x + 9y = 36

Interactive button. Assistance may be required.

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-2x + 5y = 20

Interactive button. Assistance may be required.

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4x - 11y = -44

Interactive button. Assistance may be required.

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x - y = -4

Interactive button. Assistance may be required.

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-4x + 5y = 20

Interactive button. Assistance may be required.

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-2x + 3y = 12