Question

which of the following equations match the given graph?
$y > -\frac{3}{4}x + 3$
$y < -\frac{3}{4}x + 3$
$y \leq -\frac{3}{4}x + 3$
$y \geq -\frac{3}{4}x + 3$

Explanation:

Step1: Identify the line equation

The line has slope $-\frac{3}{4}$ and y-intercept 3, so its equation is $y = -\frac{3}{4}x + 3$.

Step2: Check line type and shading

The line is solid, so the inequality includes equality ($\leq$ or $\geq$). The shaded region is above the line, so we use $\geq$.

Step3: Final inequality

Combine to get $y \geq -\frac{3}{4}x + 3$.

Answer:

$y \geq -\frac{3}{4}x + 3$