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Question 4 of 30

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M:C:MC:SET:2B

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Heart of Algebra

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Questions 3–5 refer to the following information.

The first metacarpal bone is located in the wrist. The scatterplot below shows the relationship between the length of the first metacarpal bone and height for 9 people. The line of best fit is also shown.

The figure presents a graph of a scatterplot titled “Height of Nine People and Length of Their First Metacarpal Bone,” and a line. The horizontal axis is labeled “Length of first metacarpal bone,” in centimeters, and the vertical axis is labeled “Height,” in centimeters.  There are equally spaced horizontal gridlines labeled, from bottom to top, 155 through 185, in increments of 5. There are equally spaced vertical gridlines labeled, from left to right, 4 through 5, in increments of zero point five. A straight line of best fit starts on the leftmost vertical axis at 4 comma 161.5 and stops at the intersection of the rightmost vertical gridline at 5 comma 180. There are 9 data points in the graph. From left to right, the coordinates are as follows: First point: 4 comma 157, Second point: 4.1 comma 163, Third point: 4.3 comma 175, Fourth point: 4.5 comma 171, Fifth point: 4.6 comma 173, Sixth point: 4.7 comma 173, Seventh point: 4.8 comma 172, Eighth point: 4.9 comma 183, and Ninth point: 5 comma 178

Which of the following is the best interpretation of the slope of the line of best fit in the context of this problem?

Select an Answer

The predicted height increase in centimeters for one centimeter increase in the first metacarpal bone

Correct Answer: 
Yes

The predicted first metacarpal bone increase in centimeters for every centimeter increase in height

Correct Answer: 
No

The predicted height in centimeters of a person with a first metacarpal bone length of 0 centimeters

Correct Answer: 
No

The predicted first metacarpal bone length in centimeters for a person with a height of 0 centimeters

Correct Answer: 
No

View Correct Answer

Choice A is correct. The slope is the change in the vertical distance divided by the change in the horizontal distance between any two points on a line. In this context, the change in the vertical distance is the change in the predicted height of a person, and the change in the horizontal distance is the change in the length of his or her first metacarpal bone. The unit rate, or slope, is the increase in predicted height for each increase of 1 centimeter of the first metacarpal bone.

Choice B is not the correct answer. Students who select this answer may have interpreted slope incorrectly as run over rise.

Choice C is not the correct answer. Students who select this answer may have mistaken slope for the y-intercept.

Choice D is not the correct answer. Students who select this answer may have mistaken slope for the x-intercept.

Question Difficulty: 
easy
Objective: 

Students must interpret the meaning of the slope of the line of best fit in the context provided.