Question

9a. (1 pt.) which of the following systems of inequalities represents the given graph? graph options: y < x - 4, y ≥ x - 3; y < x + 4, y ≥ -x + 3; y = x + 4, y = x + 3; y < x + 4, y > x + 3 9b. (1 pt.) which of the following systems of inequalities represents the given graph? graph options: y < 2x - 1, y ≥ 2x + 2; y < 2x + 1, y ≥ -2x + 2; y > 2x - 1, y ≤ -2x + 2; y = -2x - 1, y = x + 3 9c. (1 pt.) which of the following systems of inequalities represents the given graph? graph options: y ≤ x + 3, y ≤ -3x + 1; y < x - 3, y ≥ -3x + 1; y = x - 3, y = -3x + 1; y > -x - 3, y ≤ 3x + 1

Explanation:

9a Step1: Identify line equations

First, find the equations of the two lines. One line has a slope of 1 and y-intercept 4: $y = x + 4$. The other has a slope of -1 and y-intercept 3: $y = -x + 3$.

9a Step2: Check inequality direction

The shaded region is below $y=x+4$ (dashed line, so $y < x+4$) and above $y=-x+3$ (solid line, so $y \geq -x+3$).

9b Step1: Identify line equations

One line has a slope of 2 and y-intercept -1: $y = 2x - 1$. The other has a slope of -2 and y-intercept 2: $y = -2x + 2$.

9b Step2: Check inequality direction

The shaded region is above $y=2x-1$ (dashed line, so $y > 2x - 1$) and below $y=-2x+2$ (solid line, so $y \leq -2x + 2$).

9c Step1: Identify line equations

One line has a slope of 1 and y-intercept -3: $y = x - 3$. The other has a slope of -3 and y-intercept 1: $y = -3x + 1$.

9c Step2: Check inequality direction

The shaded region is below $y=x-3$ (dashed line, so $y < x - 3$) and above $y=-3x+1$ (solid line, so $y \geq -3x + 1$).

Answer:

9a. $\boldsymbol{y < x + 4 \\ y \geq -x + 3}$
9b. $\boldsymbol{y > 2x - 1 \\ y \leq -2x + 2}$
9c. $\boldsymbol{y < x - 3 \\ y \geq -3x + 1}$