Q13. - Algebra 2

Question

Graph each inequality.

$x+y>-5$.

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 $x+y>-5$.

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

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

$\begin{array}{l}x+y=-5\\ y=-x-5\end{array}$

 

Find the slope intercept of $x+y=-5$:

So, the slope intercept form is $y=-x-5.$

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 $x+y>-5$:

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

Step 3 – Conclusion

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

 

Graphical representation of