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

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Graphing a Line Using its Slope and y-Intercept

Example

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

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

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

Step 2 — Identify the slope and y-intercept. The coefficient of $x$ is $-1$ , so the slope is $m = -1$ . The constant term is $4$ , so the y-intercept is $(0, 4)$ .

Step 3 — Plot the y-intercept. Mark the point $(0, 4)$ on the coordinate plane.

Step 4 — Identify the rise and the run. Express the slope as a fraction: $m = \frac{-1}{1}$ The rise is $-1$ (down $1$ unit) and the run is $1$ (right $1$ unit).

Step 5 — Count the rise and run to mark the second point. Starting at $(0, 4)$ , move down $1$ unit and then right $1$ unit to reach $(1, 3)$ .

Step 6 — Connect the points with a line. Draw a straight line through $(0, 4)$ and $(1, 3)$ .

Checking the graph. The graph shows the line also passes through $(4, 0)$ . Substituting into the equation confirms this: $y = -(4) + 4 = 0$ . Since $0 = 0$ is true, the point $(4, 0)$ is indeed on the line, verifying the graph is correct.

This example illustrates the procedure when the slope is $-1$ : writing it as $\frac{-1}{1}$ clarifies that from any point on the line, moving down $1$ and right $1$ reaches another point on the line.

Updated 2026-05-03

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