Question

graph the inequality.
-5x + 2y > 4

Explanation:

Step1: Isolate y variable

Start by rearranging the inequality to solve for $y$.
$$-5x + 2y > 4$$
$$2y > 5x + 4$$

Step2: Solve for y completely

Divide all terms by 2 to isolate $y$.
$$y > \frac{5}{2}x + 2$$

Step3: Identify boundary line

The boundary line is the equation $y = \frac{5}{2}x + 2$. Since the inequality uses $>$ (not $\geq$), the line is dashed.

Step4: Determine shaded region

Test the origin $(0,0)$ in the inequality:
$$0 > \frac{5}{2}(0) + 2 \implies 0 > 2$$
This is false, so shade the region above the boundary line.

Answer:

1. Draw a dashed line for $y = \frac{5}{2}x + 2$ (this line has a y-intercept at $(0,2)$ and a slope of $\frac{5}{2}$, meaning it rises 5 units and runs 2 units).
2. Shade the entire region above this dashed line.