1Cademy - Writing the Inequality $$y \leq \frac{1}{2}x

Learn Before

Writing the Inequality $y \geq 2x - 1$ from Its Graph

Example

Writing the Inequality $y \leq \frac{1}{2}x - 4$ from Its Graph

To deduce the linear inequality from a graph displaying a solid boundary line defined by the equation $y = \frac{1}{2}x - 4$ and a shaded lower-right half-plane, a test point can be employed. The origin $(0, 0)$ , situated in the unshaded upper-left region, is a straightforward point to evaluate. Because it lies outside the shaded solution set, substituting $x = 0$ and $y = 0$ into the intended inequality must produce a false mathematical statement. Testing the 'less than or equal to' condition gives $0 \leq \frac{1}{2}(0) - 4$ , which simplifies to $0 \leq -4$ . This condition is false, correctly indicating that the half-plane containing the origin does not satisfy the inequality. Thus, the opposite, shaded half-plane represents the true solution set. Furthermore, the solid boundary line confirms that points directly on the line are included, verifying that the graph represents the inequality $y \leq \frac{1}{2}x - 4$ .

Updated 2026-05-06

Contributors are:

Who are from:

References

OpenStax Intermediate Algebra

Learn Before

Related