Question

Can someone help me with this? Please and thank you!

Answer 1

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:

`(y-y_1)/(x-x_1)=(y_2-y_1)/(x_2-x_1)`

In this case,

`\begin{gathered} x_1=0 \\ y_1=-2 \\ x_2=1 \\ y_2=1 \end{gathered}`

Substituting these values, we get

`\frac{y--2_{}}{x-0_{}}\leq\frac{1_{}--2_{}}{1_{}-0_{}}`
`\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}`

Therefore, the correct answer is:

`y\ge3x-2`