Answer:
The inequality that represents the graph is:
[tex]y\leq \frac{2}{3}x+2[/tex]
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:
[tex]y=mx+b[/tex]
m is the slope and can be calculated using the points chossen.
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]m=\frac{1+3}{6-0}[/tex]
[tex]m=\frac{4}{6}[/tex]
[tex]m=\frac{2}{3}[/tex]
Now, using one point we will find the b value. Let's chose (-3,0)
[tex]0=m(-3)+b[/tex]
[tex]0=(\frac{2}{3})(-3)+b[/tex]
[tex]0=-2+b[/tex]
[tex]b=2[/tex]
Then, the linear equation is:
[tex]y=\frac{2}{3}x+2[/tex]
Now, all the allowed values are below the function, therefore the inequality will be:
[tex]y\leq \frac{2}{3}x+2[/tex]
I hope it helps you!
