1Cademy - Graphing $$y = -\frac{2}{3}x - 3$$ Using its Slope and y-Intercept

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Graphing a Line Using its Slope and y-Intercept

Example

Graphing $y = -\frac{2}{3}x - 3$ Using its Slope and y-Intercept

To graph $y = -\frac{2}{3}x - 3$ , apply the six-step slope-and-y-intercept procedure.

Step 1 — Find the slope-intercept form. The equation $y = -\frac{2}{3}x - 3$ is already in the form $y = mx + b$ .

Step 2 — Identify the slope and y-intercept. The slope is $m = -\frac{2}{3}$ and the y-intercept is $(0, -3)$ .

Step 3 — Plot the y-intercept. Mark the point $(0, -3)$ on the coordinate plane.

Step 4 — Identify the rise and the run. The slope $m = -\frac{2}{3}$ gives a rise of $-2$ (down $2$ units) and a run of $3$ (right $3$ units).

Step 5 — Count the rise and run to mark the second point. Starting at $(0, -3)$ , move down $2$ units and then right $3$ units to reach $(3, -5)$ .

Step 6 — Connect the points with a line. Draw a straight line through $(0, -3)$ and $(3, -5)$ .

This example demonstrates the procedure when the slope is a negative fraction: the negative numerator means each step moves downward, while the positive denominator moves to the right.

Updated 2026-04-21

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OpenStax Elementary Algebra

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