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 - 5 )

Explanation:

Step1: Identify boundary line type

The inequality is $y > \frac{1}{2}x - 5$. Since the symbol is $>$ (not $\geq$), the boundary line is dashed (points on the line are not solutions).

Step2: Find intercepts of boundary line

x-intercept (set $y=0$):

$0 = \frac{1}{2}x - 5$
$\frac{1}{2}x = 5$
$x = 10$
So the x-intercept is $(10, 0)$.

y-intercept (set $x=0$):

$y = \frac{1}{2}(0) - 5$
$y = -5$
So the y-intercept is $(0, -5)$.

Step3: Graph the boundary line

Plot the points $(10, 0)$ and $(0, -5)$, then draw a dashed straight line through them.

Step4: Select solution region

Test a point not on the line, e.g., $(0,0)$:
$0 > \frac{1}{2}(0) - 5$
$0 > -5$, which is true. So shade the region above the dashed line (where $(0,0)$ lies).

Answer:

1. Set the line type to Dashed (not Solid).
2. Graph the dashed line through intercepts $(10, 0)$ and $(0, -5)$.
3. Shade the region above this dashed line to represent the solution set of $y > \frac{1}{2}x - 5$.