Question

Sketch the graph of the inequality. 3y − x ≥ 9

Answer 1

The graph of inequality is shown below.

Explanation:

The given inequality is

`3y-x\geq 9`

Related equation is

`3y-x=9`

At x=0,

`3y-0=9\Rightarrow y=3`

At y=0,

`3(0)-x=9\Rightarrow x=-9`

Plot (0,3) and (-9,0) on coordinate plane and connect them by a straight line.

Check the inequality for (0,0).

`3(0)-(0)\geq 9`

`0\geq 9`

This statement is false. So, (0,0) is not included in the shaded region.

The graph of inequality is shown below.