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Lines and Slope: Chameleon Graphing

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Lines and Slope || Chameleon Home || Ask Dr. Math
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Graphing Points First

Often, you must use an equation to graph a line. For example, somebody might ask you to graph the line 4x + 2y = 8. When this happens, you have to find some points on the line before you can graph it.

Let's ask Joan to graph 2x + y = 6.

First, Joan needs to find values of x and y that make this equation true. She decides to let x = 0.

Now that Joan has chosen a value for x, she needs to find y, so she substitutes 0 into the original equation:

    2x + y = 6
    2*0 + y = 6
    0 + y = 6
    y = 6.

Joan has found that when x = 0, y = 6. She can graph this information as the point (0, 6):

point (0, 6)

If you need practice graphing points, visit Joan's brother, Sam.

Joan needs two points before she can graph a line, so she has to find another set of values for x and y. She decides to try making y = 0. This time, she substitutes 0 into her equation for y:

    2x + y = 6
    2x + 0 = 6
    2x = 6
    x = 3

Joan has found that (x = 3, y = 0) makes her equation true, so she graphs the point (3, 0).

point (0, 6) and point (3, 0)

Now that Joan knows where two points are, she can graph her line. She crawls up the y-axis until she reaches the first point, then sticks her tongue straight into the second point.

Joan's tongue from point (0, 6) to point (3, 0)

The straight part of Joan's tongue leaves a sticky green mark behind. She adds arrows to this line and labels it with her equation, then goes looking for a fly.

the line 2x + y = 6

Joan has graphed 2x + y = 6.

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