Question

1. directions

first, select the line a button to graph the line and choose a line style. then, select the solution set button and choose the desired region.
graph the following inequality ( y > \frac{1}{2}x - 1 )

Explanation:

Step1: Identify line type

The inequality is $y \geq \frac{1}{2}x - 4$. Since the symbol is $\geq$ (includes equality), use a solid line.

Step2: Find intercepts of the line

y-intercept: Set $x=0$

$y = \frac{1}{2}(0) - 4 = -4$
So the point is $(0, -4)$.

x-intercept: Set $y=0$

$0 = \frac{1}{2}x - 4$
$\frac{1}{2}x = 4$
$x = 8$
So the point is $(8, 0)$.

Step3: Plot and draw the line

Plot points $(0, -4)$ and $(8, 0)$, then draw a solid straight line through them.

Step4: Choose solution region

Test a point not on the line, e.g., $(0,0)$:
$0 \geq \frac{1}{2}(0) - 4$
$0 \geq -4$, which is true. So shade the region above the solid line.

Answer:

1. Use a solid line to graph $y = \frac{1}{2}x - 4$ (passing through $(0, -4)$ and $(8, 0)$).
2. Shade the region above this solid line.