1Cademy - Graphing $$y = -3x$$ by Plotting Points

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Graphing a Linear Equation by Plotting Points

Example

Graphing $y = -3x$ by Plotting Points

To graph $y = -3x$ using the Point-Plotting Method, follow the three standard steps:

Step 1 — Find three solution points. Since $y$ is already isolated, choose convenient values for $x$ and compute $y$ :

$x = 0$ : $y = -3(0) = 0$ , giving $(0, 0)$
$x = 1$ : $y = -3(1) = -3$ , giving $(1, -3)$
$x = -2$ : $y = -3(-2) = 6$ , giving $(-2, 6)$

Step 2 — Plot the points. Mark $(0, 0)$ , $(1, -3)$ , and $(-2, 6)$ on a rectangular coordinate system. All three points fall on the same straight line, confirming the calculations are correct.

Step 3 — Draw the line. Connect the three points with a straight line, extend it across the grid, and add arrows on both ends. The resulting line is the graph of $y = -3x$ .

Notice that this equation has no constant term — only the variable term $-3x$ . As a result, when $x = 0$ the equation gives $y = 0$ , so the line passes through the origin $(0, 0)$ .

Updated 2026-04-21

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OpenStax Elementary Algebra

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