The Solution:
Given:
We are to write an inequality in slope-intercept form for the graph.
By the formula for the equation of a line, we have:
[tex]\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}[/tex]
In this case,
[tex]\begin{gathered} x_1=0 \\ y_1=-2 \\ x_2=1 \\ y_2=1 \end{gathered}[/tex]
Substituting these values, we get
[tex]\frac{y--2_{}}{x-0_{}}\leq\frac{1_{}--2_{}}{1_{}-0_{}}[/tex][tex]\begin{gathered} \frac{y+2_{}}{x_{}}\ge\frac{1_{}+2_{}}{1_{}_{}} \\ \\ \frac{y+2_{}}{x_{}}\ge3 \\ \\ \text{ Multiplying both sides by x.} \\ y+2\ge3x \\ y\ge3x-2 \end{gathered}[/tex]
Therefore, the correct answer is:
[tex]y\ge3x-2[/tex]
