1

Problem

The scatterplot above shows the number of grams of both total protein and total fat for eight sandwiches on a restaurant menu. The line of best fit for the data is also shown. According to the line of best fit, which of the following is closest to the predicted increase in total fat, in grams, for every increase of 1 gram in total protein?

2

Step

The predicted increase in total fat, in grams:

Every increase of 1 gram in total protein is represented by the slope of the line of best fit

3

Step

Any two points on the line can be used to calculate the slope of the line as the change in the total protein.

4

Step

For instance, it can be estimated that the points (20, 34) and (30, 48) are on the line of best fit.

5

Step

\$"Slope of the line" = (Y2 - Y1) / (X2 - X1)\$

6

Step

The slope of the line that passes through them is

\$(48 - 34) / (30 - 20)\$

=\$(14) / (10)\$, or 1.4

7

Solution

Therefore, by comparing the options given 1.5 is the closest to the slope of the line.

8

Sumup

Please summarize steps

Choices

9

Choice-A

The slope of the line of best fit is 2.5. This means that for every increase of 1 gram in total protein, the predicted increase in total fat is 2.5 grams

Wrong 2.5

10

Choice-B

This option suggests that the predicted increase in total fat for every increase of 1 gram in total protein is 2 grams. However, this value does not align with the slope of the line of best fit observed in the scatterplot

Wrong 2

11

Choice-C

This option suggests a predicted increase of 1.5 grams in total fat for every 1 gram increase in total protein. Based on the scatterplot and the slope of the line of best fit, this value appears to be the closest to the observed relationship between total protein and total fat

Correct 1.5

12

Choice-D

This option proposes a predicted increase in total fat of 1 gram for every increase of 1 gram in total protein. However, this contradicts the slope of the line of best fit, which indicates a different relationship between protein and fat content

Wrong 1

13

Answer

Option

C

14

Sumup

Please summarize choices