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, - 8)) and ((6,0)). The slope formula is (m=\frac{y_2 - y_1}{x_2 - x_1}). Substitute (x_1 = 0,y_1=-8,x_2 = 6,y_2 = 0) into the formula: (m=\frac{0-(-8)}{6 - 0}=\frac{8}{6}=\frac{4}{3}).

Step2: Find the equation of the line in slope - intercept form

The slope - intercept form is (y=mx + b), where (m) is the slope and (b) is the (y) - intercept. We know (m=\frac{4}{3}) and (b=-8), so the equation of the line is (y=\frac{4}{3}x-8).

Step3: Determine the inequality symbol

The line is dashed (so the inequality is either (>) or (<)) and the shaded region is above the line. So the inequality is (y>\frac{4}{3}x - 8).

Answer:

(y>\frac{4}{3}x - 8)