1Cademy - Graphing the Line with y-Intercept $$2$$ and Slope $$-\frac{2}{3}$$

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Graphing a Line Given a Point and the Slope

Example

Graphing the Line with y-Intercept $2$ and Slope $-\frac{2}{3}$

To graph a line whose y-intercept is $2$ and whose slope is $m = -\frac{2}{3}$ , apply the four-step point-and-slope procedure using the y-intercept as the starting point.

Step 1 — Plot the given point. The y-intercept $2$ corresponds to the point $(0, 2)$ . Mark it on the coordinate plane.

Step 2 — Identify the rise and the run. Write the slope as a fraction:

$m = -\frac{2}{3} = \frac{-2}{3}$

The rise is $-2$ (down $2$ units) and the run is $3$ (right $3$ units).

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

Step 4 — Connect the points with a line. Draw a straight line through $(0, 2)$ and $(3, 0)$ .

Checking with a third point. Because the negative sign in a fraction can be placed in either the numerator or the denominator, $-\frac{2}{3}$ can also be written as $\frac{2}{-3}$ . Returning to $(0, 2)$ and counting up $2$ units and then left $3$ units locates a third point at $(-3, 4)$ . If this point falls on the same line, the graph is confirmed correct.

Updated 2026-04-21

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OpenStax Elementary Algebra

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