Q26. - Algebra 2

Question

Graph each inequality.

$y>\left|4x\right|$.

Step-by-Step Solution

Answer

The graph of the inequality is shown below:

Step 1 – Find the boundary line equation of the given equation.

Consider the inequality $y>\left|4x\right|$.

The boundary line equaton is $y=\left|4x\right|$.

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

Step 2 – Choose a test point and test the inequality.

Choose the test point as $\left(0,1\right).$

Substitute $x=0,y=1$in $y>\left|4x\right|$:

$\begin{array}{l}y>\left|4x\right|\\ 1>\left|4\left(0\right)\right|\text{\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}substitute 0 for }x,1\text{ for }y\\ 1>0\text{\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}true}\end{array}$

Step 3 – Conclusion

Since, $1>0$results a true inequality, so, shade the region that contains the point $\left(0,1\right).$

Graphical representation of $y>\left|4x\right|$: