Which linear inequality is represented by the graph?y ≤ 2x + 4y ≤ x + 3y ≥ x + 3y ≥ 2x + 3

Accepted Solution

Answer [tex]y\leq \frac{1}{2} x+3[/tex]Explanation First we are going to find the equation of the solid line passing trough the points (0, 3) and (2, 4).Using the slope formula:[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex][tex]m=\frac{4-3}{2-0}[/tex][tex]m=\frac{1}{2}[/tex]Now we can use the point slope formula to complete the line equation:[tex]y-y_{1}=m(x-x_{1})[/tex][tex]y-3=\frac{1}{2} (x-0)[/tex][tex]y-3=\frac{1}{2}x[/tex][tex]y=\frac{1}{2}x+3[/tex]Since the shaded region is bellow the line [tex]y=\frac{1}{2}x+3[/tex], the inequality represented in the graph is [tex]y\leq \frac{1}{2} x+3[/tex].