Question

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

Answer 1

The inequality that represents the graph is:

`y\leq (2)/(3)x+2`

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=(y_(2)-y_(1))/(x_(2)-x_(1))`

`m=(1+3)/(6-0)`

`m=(4)/(6)`

`m=(2)/(3)`

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

`0=m(-3)+b`

`0=((2)/(3))(-3)+b`

`0=-2+b`

`b=2`

Then, the linear equation is:

`y=(2)/(3)x+2`

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

`y\leq (2)/(3)x+2`

I hope it helps you!