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 the points $(0, 2)$ and $(1, 0)$. The slope $m$ is calculated as $\frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - 2}{1 - 0} = -2$. The y-intercept $b$ is 2 (since the line crosses the y-axis at $(0, 2)$). So the equation of the line is $y = -2x + 2$.

Step2: Determine the inequality symbol

The line is dashed, so the inequality is either $y > -2x + 2$ or $y < -2x + 2$. The shaded region is above the line, so we use the greater than symbol. Thus, the inequality is $y > -2x + 2$.

Answer:

$y > -2x + 2$