Question

Use the table to answer the question.

x
(Miles Run) y
(Weight in Pounds)
10 130
1 200
3 167
5 145
8 135
The weight of a cheetah can be based on the number of miles they run a day. The line of best fit for this dataset is y=195−7.3x
. The table represents the scatter plot of data. Find the weight of a cheetah that runs 7 miles, and state whether extrapolation or interpolation is occurring.

(1 point)
Responses

143.9 pounds and interpolation
143.9 pounds and interpolation

130 pounds and extrapolation
130 pounds and extrapolation

143.9 pounds and extrapolation
143.9 pounds and extrapolation

130 pounds and interpolation
130 pounds and interpolation
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Answer 1

To find the weight of a cheetah that runs 7 miles using the line of best fit \( y = 195 - 7.3x \), we can substitute \( x = 7 \) into the equation:

\[
y = 195 - 7.3 \times 7
\]

Calculating the right side:

\[
y = 195 - 51.1
\]
\[
y = 143.9
\]

So, the weight of a cheetah that runs 7 miles is **143.9 pounds**.

Next, we need to determine whether we are performing interpolation or extrapolation.

- **Interpolation** occurs when we estimate a value within the range of the data points provided.
- **Extrapolation** occurs when we estimate a value outside the range of the data points provided.

Given the data points for miles run (0, 1, 3, 5, 8, 10), 7 miles is within that range. Therefore, we are performing interpolation.

The correct response is:

**143.9 pounds and interpolation.**