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1.1 Linear Functions - Slope calculation and interpretation
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The line graphed in the xy-plane below models the total cost, in dollars, for a cab ride, y, in a certain city during nonpeak hours based on the number of miles traveled, x.

The figure presents the graph of a line in the x y plane titled “Total Cost for a Cab Ride.” The x axis is labeled “Distance traveled, in miles,” and the integers 0, 5, and 10 are indied. There are vertical gridlines at each integer from 1 through 10. The y axis is labeled “Cost, in dollars,” and the integers 0, 5, 10, and 15 are indied. There are horizontal gridlines at each integer from 1 through 15. The line begins on the y axis at the point with coordinates 0 comma 3, and slants upward and to the right. It passes through the point with coordinates 5 comma 13.

According to the graph, what is the cost for each additional mile traveled, in dollars, of a cab ride?

A.

$2.60

B.

$3.00

C.

$5.00

D.

$2.00

The line graphed in the xy -plane below models the total cost, in dollars, for a

Medium-difficulty · SAT Math · Linear Functions — Slope calculation and interpretation. Read the question above, select your answer, and check the full explanation below to understand exactly why the correct choice works.

Answer explanation

Choice A is correct. The cost of each additional mile traveled is represented by the slope of the given line. The slope of the line can be calculated by identifying two points on the line and then calculating the ratio of the change in y to the change in x between the two points. Using the points with coordinates 1 comma 5 and 2 comma 7, the slope is equal to the fraction with numerator 7 minus 5, and denominator 2 minus 1, end fraction, or 2. Therefore, the cost for each additional mile traveled of the cab ride is $2.00.

Choice B is incorrect and may result from calculating the slope of the line that passes through the points with coordinates 5 comma 13 and 0 comma 0. However, the point with coordinates 0 comma 0 does not lie on the line shown. Choice C is incorrect. This is the y-coordinate of the y-intercept of the graph and represents the flat fee for a cab ride before the charge for any miles traveled is added. Choice D is incorrect. This value represents the total cost of a 1-mile cab ride.

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