Question

graph the inequality on a plane. (click to shade a region below or above the line).
$y < \frac{3}{2}x + 2$
toggle lines solidity
not quite
thats not it. try again. score: 0%

Explanation:

Step1: Identify line type

The inequality uses $<$, so the boundary line $y=\frac{3}{2}x+2$ is dashed, which is already correct in the graph.

Step2: Test a point for shading

Use the origin $(0,0)$: substitute into $y < \frac{3}{2}x + 2$:
$0 < \frac{3}{2}(0) + 2$ simplifies to $0 < 2$, which is true.

Step3: Correct shading region

Since $(0,0)$ satisfies the inequality and lies below the line, shade the region below the dashed line $y=\frac{3}{2}x+2$.

Answer:

1. Keep the dashed boundary line $y=\frac{3}{2}x+2$ (it is already correctly formatted as dashed for the $<$ inequality).
2. Shade the entire region below this dashed line (the current shaded region above the line is incorrect; the valid region includes points like the origin $(0,0)$ that satisfy the inequality).