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

Explanation:

Step1: Find the slope of the line

The line passes through points ((4, 0)) and ((0, -6)). The slope (m) is calculated as (m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{-6 - 0}{0 - 4}=\frac{-6}{-4}=\frac{3}{2}).

Step2: Determine the y - intercept

The line crosses the y - axis at ((0, -6)), so the y - intercept (b=-6). The equation of the line in slope - intercept form is (y = mx + b), so the line equation is (y=\frac{3}{2}x-6).

Step3: Determine the inequality symbol

The shaded region is above the line (since the green area is above the line (y = \frac{3}{2}x-6)) and the line is solid (so the inequality includes equality). So the inequality is (y\geq\frac{3}{2}x - 6).

Answer:

(y\geq\frac{3}{2}x - 6)