Question

Graph each inequality.

25.$y\le \left|x\right|$.

Short answer

The graph of the inequality is shown below:

Step-by-step solution

– Find the boundary line equation of the given equation.

Consider the inequality $y\le \left|x\right|$.

The boundary line equaton is $y=\left|x\right|$.

Here the inequality is $\le$, graph the boundary line as a solid line.

– Choose a test point and test the inequality.

Choose the test point as $\left(0,0\right).$

Substitute $x=0,y=0$in $y\le \left|x\right|$:

$\begin{array}{l}y\le \left|x\right|\\ 0\le \left|0\right|\text{\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}substitute0for}x,0\text{for}y\\ 0\le 0\text{\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}true}\end{array}$

– Conclusion

Since, $0\le 0$results a true inequality, so, shade the region that contains the point $\left(0,0\right).$

Graphical representation of $y\le \left|x\right|$: