Question

which point below is not part of the solution set? (20, -5) (-1, -3) (0, 0) (5, 1)

Explanation:

Step1: Identify boundary line equation

First, find the line through intercepts (0, -2) and (10, -1): slope $m=\frac{-1-(-2)}{10-0}=\frac{1}{10}$. Equation: $y=\frac{1}{10}x - 2$, or $x - 10y = 20$.

Step2: Test inequality direction

Test (0,0): $0 - 10(0)=0 < 20$, and (0,0) is in the shaded region, so inequality is $x - 10y \leq 20$.

Step3: Test each point

For (20, -5):

$20 - 10(-5)=20+50=70 \leq 20$? No, wait correction: shaded region is above the line, so inequality is $y \geq \frac{1}{10}x - 2$. Test (20,-5): $-5 \geq \frac{20}{10}-2 \to -5 \geq 0$? No, correction: look at graph, shaded region is the middle area. Re-test (-1,-3):
$-3 \geq \frac{-1}{10}-2 \to -3 \geq -2.1$? This is false.

For (0,0):

$0 \geq 0 - 2 \to 0 \geq -2$: true.

For (5,1):

$1 \geq \frac{5}{10}-2 \to 1 \geq -1.5$: true.

For (20,-5):

$-5 \geq \frac{20}{10}-2 \to -5 \geq 0$? No, correction: graph shows shaded region is between two lines. The lower line is $y=-2$, upper line $y=\frac{1}{10}x - 1$. Test (-1,-3): $-3 < -2$, so it is below the lower shaded boundary, not in the solution set.

Answer:

(-1, -3)