To determine the average rate of change between the points (-4,-7) and (4,-3), we need to calculate the rate at which the y-coordinate changes with respect to the x-coordinate. Here's the step-by-step solution:
1. Identify the coordinates: We have two points, [tex]\((-4, -7)\)[/tex] and [tex]\( (4, -3) \)[/tex].
- The first point is [tex]\((x_1, y_1) = (-4, -7)\)[/tex].
- The second point is [tex]\((x_2, y_2) = (4, -3)\)[/tex].
2. Calculate the change in y ([tex]\(\Delta y\)[/tex]):
[tex]\[
\Delta y = y_2 - y_1 = -3 - (-7)
\][/tex]
Simplifying this:
[tex]\[
\Delta y = -3 + 7 = 4
\][/tex]
3. Calculate the change in x ([tex]\(\Delta x\)[/tex]):
[tex]\[
\Delta x = x_2 - x_1 = 4 - (-4)
\][/tex]
Simplifying this:
[tex]\[
\Delta x = 4 + 4 = 8
\][/tex]
4. Calculate the average rate of change:
The formula for the average rate of change is given by [tex]\(\Delta y / \Delta x\)[/tex]:
[tex]\[
\text{Average rate of change} = \frac{\Delta y}{\Delta x} = \frac{4}{8} = 0.5
\][/tex]
5. Round the average rate of change to the nearest hundredths place:
Since our average rate of change is already at 0.5, and it doesn't need further adjustment for the hundredths place, the rounded value remains the same:
[tex]\[
0.5
\][/tex]
So, the average rate of change between the points (-4,-7) and (4,-3), rounded to the nearest hundredths place, is 0.5.
