Answer:
[tex]y\geq 4x-6[/tex]
Step-by-step explanation:
We have been given graph of an inequality. We are asked to find the inequality represented by the given graph.
First of all, we need to find equation of boundary line of our given inequality.
Let us find slope of line using points (2,2) and [tex](0,-6)[/tex].
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{-6-2}{0-2}[/tex]
[tex]m=\frac{-8}{-2}[/tex]
[tex]m=4[/tex]
We can see that y-intercept of boundary line is [tex]-6[/tex], so equation of boundary line would be [tex]y=4x-6[/tex].
We can see that boundary line is a solid line,so the points on one side of boundary line will be [tex]y\leq 4x-6[/tex] and points on other side would be [tex]y\geq 4x-6[/tex].
Now, we will test point (0,0) in both inequalities to see which inequality satisfies our given graph.
[tex]y\geq 4x-6[/tex]
[tex]0\geq 4(0)-6[/tex]
[tex]0\geq 0-6[/tex]
[tex]0\geq-6[/tex]
Since point (0,0) is in shaded region for our given inequality and inequality [tex]y\geq 4x-6[/tex] includes point (0,0), therefore, the inequality [tex]y\geq 4x-6[/tex] represents our given graph.
