inear Models Quick Check

Question

5 of 55 of 5 Items

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

130 pounds and interpolation
130 pounds and interpolation

143.9 pounds and extrapolation
143.9 pounds and extrapolation

143.9 pounds and interpolation
143.9 pounds and interpolation

130 pounds and extrapolation

Answer 1

To find the weight of a cheetah that runs 7 miles, we can use the line of best fit given by the equation \( y = 195 - 7.3x \).

Substituting \( x = 7 \):

\[ y = 195 - 7.3(7) \] \[ y = 195 - 51.1 \] \[ y = 143.9 \]

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

Next, we need to determine whether this instance is extrapolation or interpolation. The data provided in the table has mile values of \( 1, 3, 5, 8, \) and \( 10 \). Since 7 miles falls between 5 and 8 miles, this means we are estimating a value that is within the range of the provided data points. Therefore, this is an example of interpolation.

The correct response is:

143.9 pounds and interpolation.