(-5, 2) ,(4, 2)

Find the slope of the line

0

Step-by-step explanation:

Slope (m) is defined by the formula change in y divided by the change in x. You could denote "change in" using Δ (delta).

The change in y is your final postion along the y-axis, subtracted by your initial position on the y axis.

The change in x is your final position among the x-axis, subtracted by your initial position.

Think of these two sets of coords like two positions. Your final y was 2, and your initial was also 2. Do 2 - 2 to get 0. We dont even need to solve for delta x because 0 divided by anything is zero. Therefore your slope will be 0. That basically means you have a critical point of the function. The tangent line will be completely horizontal along that interval of coords.

To find the slope of the line, I will be showing you the table method.

To find the slope of the line using the table method,

we start by making a table for our ordered pairs.

We will put the x values in the left column

and the y values in the right column.

Our first ordered pair is (-5, 2), so we put a

-5 in the x column and a 2 in the y column.

Our second ordered pair is (4, 2), so we put a

4 in the x column and a 2 in the y column.

Next, remember that the slope or m, is always equal to

the rate of change or the change in y over the change in x.

Using our table, we can see that the y values

go from 2 to 2 so the change in y is 0.

The x values go from -5 to 4 so the change in x is 9.

Therefore, the rate of change, or the change in y

over the change in x is 0/9 which simplifies 0.

This means that the slope is also equal to 0.