Question

5. Which inequality is represented by the graph?8642-8 6 4 2-23468x-4-60 4x - 2y > 124x - 2y < 124x + 2y > 124x + 2y < 12

Answer 1

`\begin{gathered} For\text{ }4x-2y<12 \\ As\text{ equality }to\text{ find intercepts} \\ 4x-2y=12 \\ \text{when x=0} \\ 4(0)-2y=12 \\ -2y=12 \\ y\text{ =}(12)/(-2) \\ y=-6 \\ Intercept1(0,-6) \\ \text{When y=0} \\ 4x-2(0)=12 \\ 4x=12 \\ x=(12)/(4) \\ x=3 \\ \text{Interpcet 2 (3,0)} \\ Choo\sin g\text{ a point }to\text{ prove the inequality} \\ P(8,4) \\ 4(8)-2(4)<12 \\ 32-8<12 \\ 24<12,\text{ this is false, hence the solution is on the other side} \\ \text{Therefore the graph represents the inequality }4x-2y<12 \end{gathered}`