PSAT Math Multiple-Choice Question 647: Answer and Explanation

Question: 647

If x represents the age and y represents the average hours of sleep, which of the following gives the equation of the best-fit line for the survey results?

• A. y = -0.6x + 7.8
• B. y = 0.8x + 7.8
• C. y = -0.6x + 16.2
• D. y = -1.9x + 16.2

Correct Answer: C

Explanation:

(C) An equation of a line is given by y = mx + b, where m is the slope and b is the y-intercept. The formula for slope is calculated by finding the rise over the run, which is illustrated by this formula:

Plug in values for the endpoints:

Thus, the slope is approximately -0.6, so we can rule out choices (B) and (D).

Next, we need to determine the y-intercept b. To do this, we can plug a particular point on the line into the equation and solve for b. For instance, (14, 7.8) appears to be a point on the line. Plugging these values into the equation gives:

7.8 = -0.6(14) + b

So 7.8 = -8.4 + b.

Adding 8.4 to both sides gives 16.2 = b. Therefore, choice (C) must be correct.

With this graph, you cannot find the y-intercept, b, just by looking at the where the line crosses the y-axis. On this graph, the y-axis crosses the x-axis at 14, not at 0. However, the y-intercept is, by definition, the value of y when the value of x equals 0.