Question

of a linear inequality. write the inequality in slope - intercept form.
write your answer with y first, followed by an inequality symbol. use integers, proper fractions, and improper fractions in simplest form.

Explanation:

Step1: Find the slope and y-intercept

The line passes through points \((-5, 0)\) and \((0, -5)\). The slope \(m=\frac{-5 - 0}{0 - (-5)}=\frac{-5}{5}=-1\). The y-intercept \(b = - 5\) (since it crosses the y-axis at \((0, -5)\)). The equation of the line in slope - intercept form (\(y=mx + b\)) is \(y=-x - 5\).

Step2: Determine the inequality symbol

The line is solid (so the inequality is either \(\leq\) or \(\geq\)) and the shaded region is below the line (we test a point in the shaded region, e.g., \((0, -6)\): plug into \(y\) and \(-x - 5\), \(-6\) vs \(-0 - 5=-5\). Since \(-6<-5\), the inequality is \(y\leq - x - 5\).

Answer:

\(y\leq -x - 5\)