Question

Graph each inequality.

$y>6x-2$

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 $y>6x-2$

The boundary line equaton is $y=6x-2$

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

The equation $y=6x-2$ is in slope intercept form with slope 6.

– Choose a test point and test the inequality.

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

Substitute $x=0,y=0$in $y>6x-2$

$\begin{array}{l}y>6x-2\\ 0>6\left(0\right)-2\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}substitute0for}x,0\text{for}y\\ 0>-2\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}True}\end{array}$

– Conclusion

Since, $0>-2$results a true inequality, so, shade the region that contains the point $\left(0,0\right).$

Graphical representation of $y>6x-2$