Q16. - Algebra 2

Question

Graph each inequality.

16. $x-5\backslash le y$

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 $x-5\backslash le y$

The boundary line equaton is $y=x-5$

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

The equation $y=x-5$ is in slope intercept form with slope 1.

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

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

Substitute $x=0,y=0$in $x-5\backslash le y$

$\begin{array}{l}x-5\le y\\ 0-5\le 0\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}substitute 0 for }x,0\text{ for }y\\ -5\le 0\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}True}\end{array}$

Step 3 – Conclusion

Since, $-5\le 0$results a true inequality, so, shade the region that contains the point $\left(0,0\right).$

 Graphical representation of