graph this inequality. \n$y \\leq \\frac{1}{4}x - 5$\nplot points on the boundary line. select the line to…

graph this inequality. \n$y \\leq \\frac{1}{4}x - 5$\nplot points on the boundary line. select the line to switch between solid and dotted. select a region to shade it.

graph this inequality. \n$y \\leq \\frac{1}{4}x - 5$\nplot points on the boundary line. select the line to switch between solid and dotted. select a region to shade it.

Answer

Explanation:

Step1: Identify boundary line

The boundary line is $y = \frac{1}{4}x - 5$, solid (due to $\leq$).

Step2: Find y-intercept

Set $x=0$: $y = \frac{1}{4}(0) - 5 = -5$. Point: $(0, -5)$.

Step3: Find x-intercept

Set $y=0$: $0 = \frac{1}{4}x - 5$ $\frac{1}{4}x = 5$ $x = 20$. Point: $(20, 0)$.

Step4: Test a point for shading

Use $(0,0)$: $0 \leq \frac{1}{4}(0) - 5$ → $0 \leq -5$, false. Shade opposite side of line.

Answer:

  1. Draw a solid line through points $(0, -5)$ and $(20, 0)$.
  2. Shade the region below this solid line.