Question

Enter an inequality that represents the graph in the box.

Answer 1

Answer:

$y\geq4x-6$

Step-by-step explanation:

To find the equation of an inequality from a graph, we first need to find the equation of the line. So, let's do so.

To write the equation of the line, we need two things: 1) the slope and 2) the y-intercept.

So, let's pick two points from the graph. We can pick (0,-6) and (2,2). We will find the slope using these two points.

The slope formula is:

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

Let (0,-6) be (x₁, y₁) and let (2,2) be (x₂, y₂). So, substituting, we get:

$m=\frac{2-(-6)}{2-0}$

Add in the numerator:

$m=8/2$

Divide:

$m=4$

So, the slope of our line is 4.

Note that (0,-6) is also the y-intercept. So, our y-intercept is at y=-6.

With these, we can now write our equation using slope-intercept form, given by the equation:

$y=mx+b$

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

Substitute 4 for m and -6 for b. So:

$y=4x-6$

And this is our equation.

Now, look at the shaded region and also the line.

We can see that the line is not dotted. In other words, we will have the "or equal to" in our inequality.

Also, note that the shaded region is above the line. Since it's above the line, we will use greater than.

Therefore, our sign will be "greater than or equal to.".

So, substitute this for the equal sign, and we will acquire:

$y\geq4x-6$

And we're done!