Question

clearly indicate the solution region.

1. $y \leq \frac{3}{4}x - 4$

$y > -7$

Explanation:

Step1: Graph the line $y=\frac{3}{4}x-4$

First, identify two points on the line. When $x=0$, $y=-4$; when $x=4$, $y=\frac{3}{4}(4)-4=3-4=-1$. Plot $(0,-4)$ and $(4,-1)$, then draw a solid line (since the inequality is $\leq$, the line is included in the solution).

Step2: Shade below the solid line

For $y\leq\frac{3}{4}x-4$, the solution includes all points below or on the line, so shade the region under the solid line.

Step3: Graph the line $y=-7$

This is a horizontal line passing through $(0,-7)$. Draw a dashed line (since the inequality is $>$, the line is not included in the solution).

Step4: Shade above the dashed line

For $y>-7$, the solution includes all points above the dashed line, so shade the region above $y=-7$.

Step5: Identify overlapping shaded region

The solution region is the area that is shaded both below the solid line $y=\frac{3}{4}x-4$ and above the dashed line $y=-7$.

Answer:

The solution region is the overlapping area: above the dashed horizontal line $y=-7$ and below (and on) the solid line $y=\frac{3}{4}x-4$, as indicated by the blue shaded area in the provided grid.