Question

graph the system of inequalities on the set of axes below:
$y \leq -\frac{3}{4}x + 5$
$3x - 2y > 4$

Explanation:

Step1: Rewrite 2nd inequality to slope-intercept

Rearrange $3x - 2y > 4$ to solve for $y$:
$-2y > -3x + 4$
$y < \frac{3}{2}x - 2$
(Note: Inequality flips when dividing by -2)

Step2: Graph first boundary line

For $y \leq -\frac{3}{4}x + 5$:

• Boundary: $y = -\frac{3}{4}x + 5$ (solid line, since $\leq$)
• Y-intercept: $(0, 5)$; slope: $-\frac{3}{4}$ (down 3, right 4)
• Shade below the line (since $y \leq$)

Step3: Graph second boundary line

For $y < \frac{3}{2}x - 2$:

• Boundary: $y = \frac{3}{2}x - 2$ (dashed line, since $<$)
• Y-intercept: $(0, -2)$; slope: $\frac{3}{2}$ (up 3, right 2)
• Shade below the line (since $y <$)

Step4: Identify overlapping shaded region

The solution is the area shaded by both inequalities.

Answer:

1. Draw a solid line for $y = -\frac{3}{4}x + 5$, shade below it.
2. Draw a dashed line for $y = \frac{3}{2}x - 2$, shade below it.
3. The overlapping shaded area is the solution set of the system.