Question

determine the linear inequality associated with the given solution. (first, find the equation of the line. then rewrite this equation as an inequality with the appropriate inequality sign: <, >, ≤, or ≥.) enter the linear inequality associated with the graph on the right. (type an inequality. type your answer in slope - intercept form.)

Explanation:

Step1: Find the slope of the line

The line passes through points $(-2,0)$ and $(0, - 2)$. The slope $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{-2-0}{0 + 2}=-1$.

Step2: Find the y - intercept

The line intersects the y - axis at $(0,-2)$, so the y - intercept $b=-2$.

Step3: Write the equation of the line

The equation of the line in slope - intercept form is $y=mx + b$, so $y=-x - 2$.

Step4: Determine the inequality

The line is solid and the shaded region is below the line, so the inequality is $y\leq -x - 2$.

Answer:

$y\leq -x - 2$