Question

Im not sure how to go about this one. any help is appreciated

Answer 1

Answer:

The inequality that represents the graph is:

$y\leq \frac{2}{3}x+2$

Step-by-step explanation:

First of all, we need to get the equation of the linear function. We need to choose two points using the graph.

The first point would be (-3,0)

The second point would be (6,1)

The equation of a line is:

$y=mx+b$

m is the slope and can be calculated using the points chossen.

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$m=\frac{1+3}{6-0}$

$m=\frac{4}{6}$

$m=\frac{2}{3}$

Now, using one point we will find the b value. Let's chose (-3,0)

$0=m(-3)+b$

$0=(\frac{2}{3})(-3)+b$

$0=-2+b$

$b=2$

Then, the linear equation is:

$y=\frac{2}{3}x+2$

Now, all the allowed values are below the function, therefore the inequality will be:

$y\leq \frac{2}{3}x+2$

I hope it helps you!