Question

write a two - variable linear inequality to represent the graph.

Explanation:

Step1: Find the slope of the line

The line passes through \((0, -5)\) and \((5, 0)\). The slope \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{0 - (-5)}{5 - 0}=\frac{5}{5} = 1\).

Step2: Find the equation of the line

Using the slope - intercept form \(y=mx + b\), where \(m = 1\) and \(b=-5\) (from the point \((0,-5)\)), the equation of the line is \(y=x - 5\).

Step3: Determine the inequality symbol

The line is solid (since the region includes the line, we use \(\geq\) or \(\leq\)) and the shaded region is above the line (we can test a point in the shaded region, e.g., \((0,0)\): \(0\) compared to \(0 - 5=-5\), \(0\geq - 5\)). So the inequality is \(y\geq x - 5\) or \(x - y\leq5\).

Answer:

\(y\geq x - 5\) (or \(x - y\leq5\))