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.

Remember in Algebra 1 you learned that you can graph linear equations if you have two points, or one point and a slope.

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.

Interactive exercise. Assistance may be required.Cool Math's Graphing Calculator

Instructions for the Cool Math online calculator

Using linear equations create the following graphs in your graphing calculator or with the online graphing tool.

Remember the relationship between equations and lines graphed on the coordinate plane. If you need to review how lines are graphed using the y-intercept and the slope follow the link below.

Linear Graphing Help

Hint: equations of lines that might be helpful

Slope-Intercept    y = mx + b

Point-Slope      y - y1 = m(x - x1 )

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

    Click on the blanks to check your answers.

    Interactive button. Assistance may be required.

    ____________________

    y = − 3 over 2 3 2 x

    Interactive button. Assistance may be required.

    ____________________

    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

  2. List the equations that create a graph.

    Click on the blanks to check your answers.

    Interactive button. Assistance may be required.

    ____________________

    y = − 3 over 4 3 4 x − 3

    Interactive button. Assistance may be required.

    ____________________

    y = 4 over 3 4 3 x − 4

    Interactive button. Assistance may be required.

    ____________________

    y = − 3 over 4 3 4 x + 4

    Interactive button. Assistance may be required.

    ____________________

    y = 4 over 3 4 3 x + 3

    Interactive button. Assistance may be required.

    ____________________

    y = − 3 over 4 3 4 x + 3

    Interactive button. Assistance may be required.

    ____________________

    y = − 3 over 4 3 4 x − 4

    4. List the equations that create your graph.

    Click on the blanks to check your answers.

    Interactive button. Assistance may be required.

    ____________________

    -6x + y = -16 or y = 6x − 16

    Interactive button. Assistance may be required.

    ____________________

    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.

    ____________________

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

    Interactive button. Assistance may be required.

    ____________________

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

  4. Challenge Problem

    5. List the equations that create your graph.

    Interactive button. Assistance may be required.

    ____________________

    4x + 5y = 20

    Interactive button. Assistance may be required.

    ____________________

    x + y = 4

    Interactive button. Assistance may be required.

    ____________________

    4x+ 11y = 44

    Interactive button. Assistance may be required.

    ____________________

    2x + 5y = 20

    Interactive button. Assistance may be required.

    ____________________

    4x + 9y = 36

    Interactive button. Assistance may be required.

    ____________________

    x + 2y = 8

    Interactive button. Assistance may be required.

    ____________________

    4x + 7y = 28

    Interactive button. Assistance may be required.

    ____________________

    2x + 3y = 12

    Interactive button. Assistance may be required.

    ____________________

    4x- 7y = -28

    Interactive button. Assistance may be required.

    ____________________

    x - 2y = -8

    Interactive button. Assistance may be required.

    ____________________

    -4x + 9y = 36

    Interactive button. Assistance may be required.

    ____________________

    -2x + 5y = 20

    Interactive button. Assistance may be required.

    ____________________

    4x - 11y = -44

    Interactive button. Assistance may be required.

    ____________________

    x - y = -4

    Interactive button. Assistance may be required.

    ____________________

    -4x + 5y = 20

    Interactive button. Assistance may be required.

    ____________________

    -2x + 3y = 12