Q19. - Algebra 2

Question

Graph each inequality.

$y⩾ 1$

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 $y⩾ 1$

The boundary line equaton is $y=1$

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

 

The graph of the equation $y=1$ is a horizontal line.

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 $y⩾ 1$

$\begin{array}{l}y\ge 1\\ 0\ge 1\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}substitute 0 for }x,0\text{ for }y\\ 0\ge 1\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}false}\end{array}$

Step 3 – Conclusion

Since, $0\ge 1$results a false inequality, so, shade the region that does not contain the point $\left(0,0\right).$

 Graphical representation of $y⩾ 1$