Question

this is the graph of a linear inequality. write the inequality in slope - intercept form.

Explanation:

Step1: Find the slope of the line

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

Step2: Determine the y - intercept

The y - intercept \(b\) is the value of \(y\) when \(x = 0\). From the point \((0,-2)\), we have \(b=-2\).

Step3: Write the equation of the line in slope - intercept form

The slope - intercept form of a line is \(y=mx + b\). Substituting \(m=\frac{1}{8}\) and \(b = - 2\), the equation of the line is \(y=\frac{1}{8}x-2\).

Step4: Determine the inequality symbol

The line is solid (so the inequality is either \(\geq\) or \(\leq\)) and the shaded region is below the line (since the shaded area is towards the lower part of the line). So we use the \(\leq\) symbol.

Answer:

\(y\leq\frac{1}{8}x - 2\)