Which linear inequality is represented by the graph? y < 3x + 2 y > 3x + 2 y < 1/3x + 2 y > 1/3x + 2

Accepted Solution

Answer:[tex]y>3x+2[/tex] is represented in the graph.Step-by-step explanation:To find the linear inequality for the shown graph.Steps:Finding the equation of dotted line shown in the graph.Equation of line is given by [tex]y=mx+b[/tex]where [tex]m[/tex] is slope of line and [tex]b[/tex] is y-intercept.Given points: [tex](0,2) \ and\ (-3,-7)[/tex]Slope of the line [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex][tex]m=\frac{-7-2}{-3-0}[/tex][tex]m=\frac{-9}{-3}[/tex]∴ [tex]m=3[/tex]From the given points we can see that point of y-intercept is given i.e. the point where the line intersects the y-axis  [tex](0,2)[/tex] ∴ [tex]b=2[/tex]So equation of line:[tex]y=3x+2[/tex]Since the shaded area in the graph is above the line and the line is dotted this means that [tex]y[/tex] is greater than the equation of line.So, the inequality can be given as:[tex]y>3x+2[/tex]