which inequality is represented by the graph?\n$y> -\\frac{2}{3}x + 1$\n$y< -\\frac{2}{3}x + 1$\n$y<…

which inequality is represented by the graph?\n$y> -\\frac{2}{3}x + 1$\n$y< -\\frac{2}{3}x + 1$\n$y< -\\frac{3}{2}x + 1$\n$y> -\\frac{3}{2}x + 1$

which inequality is represented by the graph?\n$y> -\\frac{2}{3}x + 1$\n$y< -\\frac{2}{3}x + 1$\n$y< -\\frac{3}{2}x + 1$\n$y> -\\frac{3}{2}x + 1$

Answer

Explanation:

Step1: Find the slope of the line

The line passes through ((0,1)) and ((2,-2)). The slope (m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{-2 - 1}{2 - 0}=\frac{-3}{2}=-\frac{3}{2}).

Step2: Determine the inequality sign

The line is dashed, so the inequality is either (y>mx + b) or (y<mx + b). Take a test - point, say ((0,0)). Substitute (x = 0) and (y = 0) into (y=-\frac{3}{2}x + 1). We get (0=-\frac{3}{2}(0)+1) → (0<1). Since ((0,0)) is in the shaded region and (0<-\frac{3}{2}(0)+1), the inequality is (y<-\frac{3}{2}x + 1).

Answer:

(y<-\frac{3}{2}x + 1) (the third option)