Question

1. $y < \frac{1}{2}x - 3$

Explanation:

Step1: Identify boundary line

The inequality is $y < \frac{1}{2}x - 3$, so the boundary is the line $y = \frac{1}{2}x - 3$. Since the inequality uses $<$, the line is dashed.

Step2: Find intercepts of boundary

• y-intercept: Set $x=0$:

$y = \frac{1}{2}(0) - 3 = -3$. So the point is $(0, -3)$.

• x-intercept: Set $y=0$:

$0 = \frac{1}{2}x - 3$
$\frac{1}{2}x = 3$
$x = 6$. So the point is $(6, 0)$.

Step3: Test a point for shading

Use the origin $(0,0)$:
$0 < \frac{1}{2}(0) - 3$ simplifies to $0 < -3$, which is false. So we shade the region not containing the origin (below the dashed line).

Answer:

1. Draw a dashed line connecting $(0, -3)$ and $(6, 0)$.
2. Shade the area below this dashed line.