this is the graph of a linear inequality. write the inequality in slope-intercept form.\nwrite your answer…

Explanation:

Step1: Find the slope of the line

The line passes through points ((0, -2)) and ((4, 0)). The slope (m) is calculated as (m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{0 - (-2)}{4 - 0}=\frac{2}{4}=\frac{1}{2}).

Step2: Determine the y-intercept

The line crosses the y - axis at ((0, -2)), so the y - intercept (b=-2). The equation of the line in slope - intercept form ((y = mx + b)) is (y=\frac{1}{2}x-2).

Step3: Determine the inequality symbol

The line is dashed, so the inequality is either (y\lt\frac{1}{2}x - 2) or (y\gt\frac{1}{2}x - 2). The shaded region is below the line, so we use the less than symbol.

Answer:

(y\lt\frac{1}{2}x - 2)