Answer:
[tex]y>3x-1[/tex]
Step-by-step explanation:
To write the inequality represented by the graph, let's first determine the equation of the line.
So, we can see that the line passes through the two points (0,-1) and (1,2).
With this, let's figure out the slope. The formula for slope is:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Let's let (0,-1) be (x₁ y₁) and let's let (1,2) be (x₂, y₂). So:
[tex]m=\frac{2-(-1)}{1-0}[/tex]
Evaluate:
[tex]m=3/1=3[/tex]
Therefore, the slope is 3.
We also know that the y-intercept is y=-1 from the point (0,-1).
So, we can use the slope-intercept form:
[tex]y=mx+b[/tex]
Where m is the slope and b is the y-intercept.
Substitute 3 for m and -1 for b. So:
[tex]y=3x-1[/tex]
Notice that the line is dotted. This means that we will not have "or equal to" for our inequality.
Now, note that the shaded region is above our line. Therefore, y must be greater than our equation. Therefore, our inequality would be:
[tex]y>3x-1[/tex]
And we're done!
