1Cademy - Graphing $$y \geq \frac{3}{4}x

Learn Before

Example

Graphing $y \geq \frac{3}{4}x - 2$

To graph the inequality $y \geq \frac{3}{4}x - 2$ , apply the three-step graphing procedure: Step 1 — Graph the boundary line. Replace the $\geq$ symbol with $=$ to obtain the boundary line $y = \frac{3}{4}x - 2$ . Because the inequality uses $\geq$ (non-strict), draw this line as a solid line to indicate that points on the line are included in the solution set. Step 2 — Test a point. Choose $(0, 0)$ since it is not on the boundary line and is easy to evaluate: $0 \stackrel{?}{\geq} \frac{3}{4}(0) - 2$ $0 \stackrel{?}{\geq} -2$ $0 \geq -2$ is true, so $(0, 0)$ is a solution of the inequality. Step 3 — Shade the correct side. Because the test point $(0, 0)$ is a solution, shade the half-plane that contains $(0, 0)$ — the region above the boundary line. This example illustrates the non-strict case: the solid boundary line shows that every point lying exactly on $y = \frac{3}{4}x - 2$ is also part of the solution set, in addition to all points in the shaded region above it.

Updated 2026-05-03

Contributors are:

Who are from:

References

Learn Before

Related

Learn After