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}{3}x - 2 )

Explanation:

Step1: Identify line type for inequality

Since the inequality is $y > \frac{1}{3}x - 2$ (strict inequality, no "equal to"), the boundary line is dashed (not solid).

Step2: Find intercepts of boundary line

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

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

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

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

Step3: Graph the boundary line

Plot points $(6, 0)$ and $(0, -2)$, then draw a dashed line through them.

Step4: Select solution region

Test a point not on the line, e.g., $(0,0)$:
$0 > \frac{1}{3}(0) - 2$
$0 > -2$, which is true. So shade the region above the dashed line.

Answer:

1. Set Line Type to Dashed (not solid).
2. Graph the dashed line through intercepts $(6, 0)$ and $(0, -2)$.
3. Shade the region above this dashed line to represent the solution set of $y > \frac{1}{3}x - 2$.