Question

Graph each inequality.

$\mathit{y}\mathbf{>}\mathit{x}\mathbf{-}\mathbf{3}$

Short answer

The graph of the given inequality$y>x-3$is:

Step-by-step solution

Step 1. Write the procedure to draw the graph of the inequality y>x−3.

Convert the inequality$y>x-3$into equality that is convert the inequality into equation.

Therefore, it is obtained that:$y=x-3$

Therefore, the equation of the boundary is $y=x-3$. The inequality$y>x-3$has no equal to sign , therefore the boundary is not included in the solution. Therefore, the boundary is denoted by dashed lines.

Draw the graph of the boundary line $y=x-3$.

Substitute 0 for$x$and find the value of $y$.

$\begin{array}{l}y=x-3\\ y=0-3\\ y=-3\end{array}$

Therefore, one of the point islocalid="1647855694559" $\left(0,-3\right)$

Substitute 0 forlocalid="1647855700131" $y$and find the value of localid="1647855709692" $x$.

$\begin{array}{c}y=x-3\\ 0=x-3\\ 3=x\end{array}$

Therefore the other point islocalid="1647855721056" $\left(3,0\right)$

Therefore, draw the graph of the boundary linelocalid="1647855725755" $y=x-3$by drawing a line passing through the pointslocalid="1647855738659" $\left(0,-3\right)$and localid="1647855743499" $\left(3,0\right)$.

Now to draw the graph of the inequality localid="1647855748786" $y>x-3$, take any point which is not on the linelocalid="1647855755655" $y=x-3$in the inequality localid="1647855760765" $y>x-3$. If the condition obtained is true, then shade the region towards that point and if the condition obtained is false, then shade the region away from the point.

Let the point belocalid="1647855767142" $\left(0,0\right)$and the pointlocalid="1647855771881" $\left(0,0\right)$is not on the line localid="1647855777141" $y=x-3$.

Substitute the point in the inequality localid="1647855782305" $y>x-3$.

$\begin{array}{c}y>x-3\\ 0>0-3\\ 0>-3\end{array}$

As, the condition obtained is localid="1647855788692" $0>-3$, which is true. Therefore, to draw the graph of the inequality localid="1647855794468" $y>x-3$, shade the region towards the point localid="1647855800820" $\left(0,0\right)$.

Step 2. Draw the graph of the given inequality y>x−3 by using the above facts.

The graph of the given inequality $y>x-3$is: