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 two points on the line

Let's take two points $(0, 5)$ and $(5,0)$ from the graph.

Step2: Calculate the slope $m$

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Substituting $(x_1,y_1)=(0,5)$ and $(x_2,y_2)=(5,0)$, we get $m=\frac{0 - 5}{5-0}=\frac{- 5}{5}=-1$.

Step3: Find the y - intercept $b$

The line crosses the y - axis at $(0,5)$, so $b = 5$. The equation of the line in slope - intercept form is $y=-x + 5$.

Step4: Determine the inequality sign

The shaded region is below the line and the line is solid. So the inequality is $y\leq -x + 5$.

Answer:

$y\leq -x + 5$