Question

this is the graph 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 of the line

The line passes through \((0, 0)\) and \((8, -2)\). The slope \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{-2 - 0}{8 - 0}=-\frac{1}{4}\).

Step2: Determine the inequality symbol

The line is solid (so the inequality includes equality) and the shaded region is below the line, so the inequality symbol is \(\leq\).

Step3: Write the slope - intercept form

The slope - intercept form of a line is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. Here, \(m =-\frac{1}{4}\) and \(b = 0\). So the inequality is \(y\leq-\frac{1}{4}x+0\), which simplifies to \(y\leq-\frac{1}{4}x\).

Answer:

\(y\leq-\frac{1}{4}x\)