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 < 3x - 6 )

Explanation:

Step1: Identify boundary line

The boundary line is $y=3x-6$, a linear equation.

Step2: Determine line style

Since the inequality is $<$ (not $\leq$), use a dashed line (points on the line are not solutions).

Step3: Find intercepts for graphing

• x-intercept: Set $y=0$, solve $0=3x-6$

$3x=6 \implies x=2$, so point $(2, 0)$

• y-intercept: Set $x=0$, solve $y=3(0)-6$

$y=-6$, so point $(0, -6)$

Step4: Test a point for solution region

Use test point $(0,0)$: $0 < 3(0)-6 \implies 0 < -6$, which is false. So shade the region below/under the dashed line (opposite of the test point).

Answer:

1. Graph the dashed line passing through $(2, 0)$ and $(0, -6)$ (this is $y=3x-6$, dashed because the inequality is strict $<$).
2. Shade the entire region that lies below this dashed line.