Which linear inequality is represented by the graph?A. y < x + 3B. y > x + 3C. y > x + 3D. y < x + 3

Accepted Solution

Answer:The correct answer option is C. [tex]y>\frac{2}{3}x+3[/tex].Step-by-step explanation:We are given a graph and we are to determine whether which linear  inequality is represented by the graph.We know that the grey part on the graph represents the the region which is not included in the inequality. Also, when x = 0, the values of y can only be less than 3.So we choose two points on the graph and we find the slope.For example, we take the points [tex](0,3)[/tex] and [tex](3,5)[/tex].Slope = [tex]\frac{5-3}{3-0} =\frac{2}{3}[/tex]which makes the equation of the line [tex]y=\frac{2}{3}x+3[/tex] and inequality [tex]y>\frac{2}{3}x+3[/tex].