graph the inequality on the axes below. y ≤ 3x - 6

Explanation:

Step1: Identify the line equation

The boundary - line is $y = 3x-6$.

Step2: Find the y - intercept

Set $x = 0$, then $y=3\times0 - 6=-6$. So the y - intercept is $(0,-6)$.

Step3: Find the x - intercept

Set $y = 0$, then $0 = 3x-6$, which gives $3x=6$ and $x = 2$. So the x - intercept is $(2,0)$.

Step4: Determine the line type

Since the inequality is $y\leq3x - 6$, the boundary - line is solid.

Step5: Test a point

Test the point $(0,0)$. Substitute $x = 0$ and $y = 0$ into the inequality: $0\leq3\times0-6$, or $0\leq - 6$, which is false. So the region that does not contain the origin $(0,0)$ is the solution region.

Answer:

Graph a solid line passing through $(0,-6)$ and $(2,0)$ and shade the region below the line.