Q17. - Algebra 2

Question

Graph each inequality.

$y\ge -4x+3$

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 $y\ge -4x+3$

The boundary line equation is $y=-4x+3$

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

The equation $y=-4x+3$ is in slope-intercept form with slope -4.

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 $y\ge -4x+3$

$\begin{array}{l}y\ge -4x+3\\ 0\ge -4\left(0\right)+3\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}substitute 0 for }x,0\text{ for }y\\ 0\ge 3\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}false}\end{array}$

Step 3 – Conclusion

Since, $0\ge 3$results a false inequality, so, shade the region that does not contain the point $\left(0,0\right).$

 Graphical representation of $y\ge -4x+3$