Question

the following graph represents an inequality. select the ordered pairs which are solutions to it. draw show your work here (-5,8) (1,2) (-6,8) (-4,1)

Explanation:

Step1: Find the equation of the boundary - line

The boundary - line passes through (0, 2) and (2, 0). The slope $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{0 - 2}{2 - 0}=-1$. Using the slope - intercept form $y = mx + b$ with $b = 2$, the equation of the line is $y=-x + 2$. Since the line is solid and the shaded region is above the line, the inequality is $y\geq -x + 2$.

Step2: Test the ordered pairs

• For $(-5,8)$: Substitute $x=-5$ and $y = 8$ into $y\geq -x + 2$. We get $8\geq-(-5)+2$, which simplifies to $8\geq5 + 2$ or $8\geq7$. This is True.
• For $(-6,8)$: Substitute $x=-6$ and $y = 8$ into $y\geq -x + 2$. We get $8\geq-(-6)+2$, which simplifies to $8\geq6 + 2$ or $8\geq8$. This is True.
• For $(1,2)$: Substitute $x = 1$ and $y = 2$ into $y\geq -x + 2$. We get $2\geq-1+2$ or $2\geq1$. This is True.
• For $(-4,1)$: Substitute $x=-4$ and $y = 1$ into $y\geq -x + 2$. We get $1\geq-(-4)+2$, which simplifies to $1\geq4 + 2$ or $1\geq6$. This is False.

Answer:

$(-5,8),(-6,8),(1,2)$