Question

graph this inequality:
$y < -\frac{2}{3}x + 4$
plot points on the boundary line. select the line to switch between solid and dotted. select a region to shade it.

Explanation:

Step1: Identify boundary line type

Since the inequality is $y < -\frac{2}{3}x + 4$ (strict inequality, no "equal to"), the boundary line $y = -\frac{2}{3}x + 4$ is dotted.

Step2: Find intercepts of boundary line

y-intercept (x=0):

$y = -\frac{2}{3}(0) + 4 = 4$
Point: $(0, 4)$

x-intercept (y=0):

$0 = -\frac{2}{3}x + 4$
$\frac{2}{3}x = 4$
$x = 4 \times \frac{3}{2} = 6$
Point: $(6, 0)$

Step3: Test a point for shading

Use test point $(0,0)$ (not on the line):
$0 < -\frac{2}{3}(0) + 4$ → $0 < 4$, which is true. Shade the region containing $(0,0)$ (below the line).

Answer:

1. Plot the dotted boundary line using points $(0, 4)$ and $(6, 0)$.
2. Shade the region below this dotted line.