Question

{50 PTS (100 Total) Each answer} Can someone please help me? I need to get it submitted soon.

Answer 1

Answer:

$y>3x-1$

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:

$m=\frac{y_2-y_1}{x_2-x_1}$

Let's let (0,-1) be (x₁ y₁) and let's let (1,2) be (x₂, y₂). So:

$m=\frac{2-(-1)}{1-0}$

Evaluate:

$m=3/1=3$

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:

$y=mx+b$

Where m is the slope and b is the y-intercept.

Substitute 3 for m and -1 for b. So:

$y=3x-1$

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:

$y>3x-1$

And we're done!