graph this inequality: \n$y \\geq \\frac{7}{6}x - 4$\nplot points on the boundary line. select the line to…

graph this inequality: \n$y \\geq \\frac{7}{6}x - 4$\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$y \\geq \\frac{7}{6}x - 4$\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 type

Since the inequality is $y \geq \frac{7}{6}x - 4$ (includes equality), use a solid line for the boundary $y=\frac{7}{6}x - 4$.

Step2: Find y-intercept of boundary

Set $x=0$: $y = \frac{7}{6}(0) - 4 = -4$ Point: $(0, -4)$

Step3: Find x-intercept of boundary

Set $y=0$: $0 = \frac{7}{6}x - 4$ $\frac{7}{6}x = 4$ $x = 4 \times \frac{6}{7} = \frac{24}{7} \approx 3.43$ Point: $\left(\frac{24}{7}, 0\right)$

Step4: Test point for shading

Use $(0,0)$ (not on the line): $0 \geq \frac{7}{6}(0) - 4$ $0 \geq -4$, which is true. Shade the region containing $(0,0)$.

Answer:

  1. Draw a solid line through the points $(0, -4)$ and $\left(\frac{24}{7}, 0\right)$ (or $(0,-4)$ and $(6, 3)$, since when $x=6$, $y=\frac{7}{6}(6)-4=7-4=3$ for easier plotting).
  2. Shade the region above (and including) this solid line, as the test point $(0,0)$ satisfies the inequality.