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 points \((-5, 0)\) and \((0, 5)\). The slope \(m\) is calculated as \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{5 - 0}{0 - (-5)}=\frac{5}{5} = 1\).

Step2: Find the y - intercept

The line crosses the y - axis at \((0, 5)\), so the y - intercept \(b = 5\). The equation of the line in slope - intercept form (\(y=mx + b\)) is \(y=x + 5\).

Step3: Determine the inequality symbol

The line is solid (so the inequality is either \(\geq\) or \(\leq\)) and the shaded region is above the line, so we use the \(\geq\) symbol.

Answer:

\(y\geq x + 5\)