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-intercept form of the line

The slope-intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. From the graph, the line passes through $(0, 5)$ (so $b = 5$) and another point, say $(-2, 0)$. The slope $m$ is calculated as $\frac{y_2 - y_1}{x_2 - x_1} = \frac{5 - 0}{0 - (-2)} = \frac{5}{2}$. So the equation of the line is $y = \frac{5}{2}x + 5$.

Step2: Determine the inequality symbol

The line is solid (since the boundary is included) and the shaded region is above the line, so the inequality symbol is $\geq$.

Step3: Write the inequality

Substituting the symbol into the line equation, we get $y \geq \frac{5}{2}x + 5$.

Answer:

$y \geq \frac{5}{2}x + 5$