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 signs (<, >, ≤, 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 assume two points \((x_1,y_1)\) and \((x_2,y_2)\) on the line from the graph. Suppose the points are \((0, 3)\) and \((3,0)\).

Step2: Calculate the slope \(m\)

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). So \(m=\frac{0 - 3}{3-0}=\frac{- 3}{3}=-1\).

Step3: Find the y - intercept \(b\)

The y - intercept is the y - value when \(x = 0\). From the point \((0,3)\), \(b = 3\).

Step4: Write the equation of the line

The slope - intercept form of a line is \(y=mx + b\), so the equation of the line is \(y=-x + 3\).

Step5: Determine the inequality sign

Since the line is solid and the region below the line is shaded, the inequality is \(y\leq -x + 3\).

Answer:

\(y\leq -x + 3\)