Question

graph the inequality on the axes below.
$y \geq -\frac{5}{4}x - 5$

Explanation:

Step1: Identify boundary line

The inequality $y \geq -\frac{5}{4}x - 5$ has a boundary line $y = -\frac{5}{4}x - 5$. Since the inequality is $\geq$, the line is solid.

Step2: Find y-intercept

Set $x=0$:
$y = -\frac{5}{4}(0) - 5 = -5$
This gives the point $(0, -5)$.

Step3: Find x-intercept

Set $y=0$:
$0 = -\frac{5}{4}x - 5$
Add 5 to both sides: $5 = -\frac{5}{4}x$
Multiply both sides by $-\frac{4}{5}$: $x = -4$
This gives the point $(-4, 0)$.

Step4: Determine shaded region

Test the origin $(0,0)$ in the inequality:
$0 \geq -\frac{5}{4}(0) - 5$
$0 \geq -5$, which is true. So shade the region containing the origin (above the solid line).

Answer:

1. Draw a solid line connecting the points $(-4, 0)$ and $(0, -5)$.
2. Shade the region above and including this solid line.