Q14. - Algebra 2

Question

Graph each inequality.

14.$3\ge x-3y$.

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$3\ge x-3y$.

The boundary line equaton is $x-3y=3$.

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

 Find the slope intercept of$x-3y=3$:

$\begin{array}{l}x-3y=3\\ -3y=3-x\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}subtract }x\text{ from both sides}\\ y=\frac{3-x}{-3}\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}divide both sides by }-3\\ y=\frac{x}{3}-1\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}simplify}\end{array}$

So, the slope intercept form is $y=\frac{x}{3}-1.$

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

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

Substitute $x=0,y=0in 3\backslash ge x-3y$

$\begin{array}{l}3\ge x-3y\\ 3\ge 0-3\left(0\right)\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}substitute 0 for }x,0\text{ for }y\\ 3\ge 0\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}True}\end{array}$

Step 3 – Conclusion

Since, $3\ge 0$results a true inequality, so, shade the region that contains the point $\left(0,0\right).$

 Graphical representation of $3\backslash ge x-3y$