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Lines and Slope: Chameleon Graphing

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Graphing Another Equation

Let's ask Joan to graph a different line: y = 4x - 2.

Joan needs to find values for x and y that make the equation true. She decides to start by substituting 0 for x, just as before.

    y = 4x - 2
    y = 4 * 0 -2
    y = 0 - 2
    y = -2

Joan's substitution tells her the equation is true when x = 0 and y = -2, so she graphs the point (0, -2).

point (0, -2)

When an equation is written like this one, it's fairly simple to find y by substituting different values for x. Joan decides to let x = 1:

    y = 4x - 2
    y = 4 * 1 - 2
    y = 4 - 2
    y = 2

Now Joan knows that x = 1, y = 2 also works, so she graphs (1, 2).

point (0, -2) and point (1, 2)

Next, Joan crawls down the y-axis and sticks her tongue straight through the two points. The straight part of her tongue will make a green trace.

Joan's tongue from point (0, -2) to point (1, 2)

Before she leaves, Joan draws arrows to show that her line continues forever. She also labels the line with the equation it came from.

line y = 4x - 2

Joan just graphed y = 4x - 2.

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