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 \((0, 1)\) and \((6, 7)\). The slope \(m\) is calculated as \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{7 - 1}{6 - 0}=\frac{6}{6} = 1\).

Step2: Determine the y - intercept

The line crosses the y - axis at \((0,1)\), so the y - intercept \(b = 1\). The equation of the line in slope - intercept form (\(y=mx + b\)) is \(y=x + 1\).

Step3: Determine the inequality symbol

The shaded region is above the line, and the line is a solid line (since the boundary is included in the solution set). So the inequality symbol is \(\geq\).

Answer:

\(y\geq x + 1\)