Question

1. graph the inequality

$y > 2x - 4$

1. graph the inequality

$5x - 2y \leq 8$

1. which points are solutions to the

inequality below?

1. which ordered pair is not a solution to the system of inequalities?

$3x + y > -3$
$x + 2y < 4$
a. (1, 1)
b. (-1, 2)
c. (4, -3)
d. (-5, 1)

Explanation:

Question 17

Step1: Identify boundary line

Boundary is $y=2x-4$ (dashed, since $>$)

Step2: Plot boundary line

Find intercepts:

• x-intercept: set $y=0$, $0=2x-4 \implies x=2$, point $(2,0)$
• y-intercept: set $x=0$, $y=-4$, point $(0,-4)$

Draw dashed line through these points.

Step3: Test a point for shading

Test $(0,0)$: $0 > 2(0)-4 \implies 0 > -4$, true. Shade region above the line.

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Question 18

Step1: Rewrite inequality for y

$5x-2y \leq 8 \implies -2y \leq -5x+8 \implies y \geq \frac{5}{2}x-4$

Step2: Plot boundary line

Boundary is $y=\frac{5}{2}x-4$ (solid, since $\geq$)
Find intercepts:

• x-intercept: set $y=0$, $0=\frac{5}{2}x-4 \implies x=\frac{8}{5}=1.6$, point $(1.6,0)$
• y-intercept: set $x=0$, $y=-4$, point $(0,-4)$

Draw solid line through these points.

Step3: Test a point for shading

Test $(0,0)$: $0 \geq \frac{5}{2}(0)-4 \implies 0 \geq -4$, true. Shade region above the line.

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Question 19

Step1: Identify the inequality

The graph shows a solid line with shaded region above it. The line has slope $1$, y-intercept $-3$, so inequality is $y \geq x-3$

Step2: Test each point

• $(0,-4)$: $-4 \geq 0-3 \implies -4 \geq -3$ → False
• $(2,-1)$: $-1 \geq 2-3 \implies -1 \geq -1$ → True
• $(4,-3)$: $-3 \geq 4-3 \implies -3 \geq 1$ → False
• $(3,2)$: $2 \geq 3-3 \implies 2 \geq 0$ → True
• $(5,-1)$: $-1 \geq 5-3 \implies -1 \geq 2$? No, wait correction: Line passes through $(0,-3)$ and $(3,0)$, so slope $\frac{0-(-3)}{3-0}=1$, equation $y=x-3$. Shaded region is above, so $y \geq x-3$. $(5,-1)$: $-1 \geq 5-3 \implies -1 \geq 2$? No, correction: Shaded region is below the line (graph shows shaded right/down). Inequality is $y \leq x-3$

Re-test:

• $(0,-4)$: $-4 \leq 0-3 \implies -4 \leq -3$ → True
• $(2,-1)$: $-1 \leq 2-3 \implies -1 \leq -1$ → True
• $(4,-3)$: $-3 \leq 4-3 \implies -3 \leq 1$ → True
• $(3,2)$: $2 \leq 3-3 \implies 2 \leq 0$ → False
• $(5,-1)$: $-1 \leq 5-3 \implies -1 \leq 2$ → True
• $(-3,-5)$: $-5 \leq -3-3 \implies -5 \leq -6$ → False

Correct answer: $(0,-4)$, $(2,-1)$, $(4,-3)$, $(5,-1)$

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Question 20

Answer:

(Graph description: Dashed line $y=2x-4$, shaded region above the line)