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 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 \((0, -2)\) (y-intercept, so \( b = -2 \)) and \((1, 0)\) (we can use this to find the slope). The slope \( m \) is calculated as \( \frac{y_2 - y_1}{x_2 - x_1} \). Using \((0, -2)\) as \((x_1, y_1)\) and \((1, 0)\) as \((x_2, y_2)\), we get \( m=\frac{0 - (-2)}{1 - 0}=\frac{2}{1}=2 \). So the equation of the line is \( y = 2x - 2 \).

Step2: Determine the inequality symbol

The shaded region is above the dashed line (dashed line means the inequality is strict, and since the blue region is above the line, we use \( > \)). So the inequality is \( y > 2x - 2 \).

Answer:

\( y > 2x - 2 \)