Question

Graph each inequality.

23.$y>\frac{1}{3}x+5$.

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 $y>\frac{1}{3}x+5$.

The boundary line equaton is $y=\frac{1}{3}x+5$.

Here the inequality is $>$, graph the boundary line as a dashed line.

The slope intercept form is $y=\frac{1}{3}x+5$with slope $\frac{1}{3}.$

– Choose a test point and test the inequality.

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

Substitute $x=0,y=0$in $y>\frac{1}{3}x+5$:

$\begin{array}{l}y>\frac{1}{3}x+5\\ 0>\frac{1}{3}\left(0\right)+5\text{\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}substitute0for}x,0\text{for}y\\ 0>5\text{\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}false}\end{array}$

– Conclusion

Since, $0>5$results a false inequality, so, shade the region that does not contain the point $\left(0,0\right).$

Graphical representation of $y>\frac{1}{3}x+5$: