1Cademy - Graphing $$y = 4x - 2$$ Using its Slope and y-Intercept

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Graphing a Line Using its Slope and y-Intercept

Example

Graphing $y = 4x - 2$ Using its Slope and y-Intercept

To graph the equation $y = 4x - 2$ , apply the six-step slope-and-y-intercept procedure.

Step 1 — Find the slope-intercept form. The equation $y = 4x - 2$ is already in the form $y = mx + b$ .

Step 2 — Identify the slope and y-intercept. Comparing with $y = mx + b$ : the slope is $m = 4$ and the y-intercept is $(0, -2)$ .

Step 3 — Plot the y-intercept. Mark the point $(0, -2)$ on the coordinate plane.

Step 4 — Identify the rise and the run. Since the slope is a whole number, express it as a fraction over $1$ :

$m = \frac{\text{rise}}{\text{run}} = \frac{4}{1}$

The rise is $4$ and the run is $1$ .

Step 5 — Count the rise and run to mark the second point. Starting at $(0, -2)$ , move up $4$ units and then right $1$ unit to reach $(1, 2)$ .

Step 6 — Connect the points with a line. Draw a straight line through $(0, -2)$ and $(1, 2)$ . This line is the graph of $y = 4x - 2$ .

This example demonstrates the procedure when the slope is a positive integer: writing it as $\frac{4}{1}$ makes the rise and run easy to read off directly.

Updated 2026-04-21

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OpenStax Elementary Algebra

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