Question

Which linear inequality can be used to represent the graph?

Answer 1

The linear inequality that can represent the graph is;

`y>2x-3`

Step-by-step explanation:

To get the inequality represented on the graph, let us firstly find the equation of the broken line;

Recall that the equation of a line can be represented by the equation;

`y=mx+c`

Where;

m = slope

c = y-intercept

From the graph;

The y-intercept of the line is at y=-3

`c=-3`

The slope of the line is;

`\begin{gathered} m=\frac{\text{rise}}{\text{run}}=(4)/(2) \\ m=2 \end{gathered}`

so, the equation of the line is;

`y=2x-3`

We can see on the graph that the shaded part is above the line and also the line is a broken line.

Therefore, the linear inequality that can represent the graph is;

`y>2x-3`