The sterplot above shows the number of visitors to a railroad museum in Pennsylvania each year from 1968 to 1980,

Question

The figure presents a sterplot titled “Railroad Museum Visitors.” The horizontal axis is labeled “Years since 1968,” and the numbers 0 through 15, in increments of 5, are indied. The vertical axis is labeled “Annual visitors,” and the numbers 0 through 80,000, in increments of 20,000, are indied. There are 13 data points indied on the sterplot. The data points begin at the point with approximate coordinates 0 comma 5,000, and trend upward and to the right until they end at the point with approximate coordinates 12 comma 75,000. A line of best fit is drawn. The line begins at the point with approximate coordinates 0 comma 16,000, and slants upward and to the right. It passes through the point with approximate coordinates 5 comma 40,000, and continues upward until it ends at the point with approximate coordinates 12 comma 74,000.

The sterplot above shows the number of visitors to a railroad museum in Pennsylvania each year from 1968 to 1980, where t is the number of years since 1968 and n is the number of visitors. A line of best fit is also shown. Which of the following could be an equation of the line of best fit shown?

A.

$n equals, 16,090, plus 4,680, t$

B.

$n equals, 4,690, plus 16,090, t$

C.

$n equals, 16,090, plus 9,060, t$

D.

$n equals, 9,060, plus 16,090, t$

Accepted Answer

Choice A is correct. An equation of a line of best fit can be written in the form , where a is the y -intercept of the line and b is the slope. In the sterplot shown, the line of best fit intersects the y -axis just over halfway between 10,000 and 20,000, or approximately 16,000. The line of best fit also intersects the graph at . Using the slope formula and two points that lie on the graph such as and , the slope can be approximated as , or 4,800. Only choice A has a y -intercept near the estimate of 16,000 and a slope near the estimate of 4,800. Therefore, an equation of the line of best fit could be . Choice B is incorrect because the values for the slope and the y -coordinate of the y -intercept are switched. Choice C is incorrect because the value for the slope is approximately double the actual slope. Choice D is incorrect because the values for the slope and the y- intercept are switched and because the slope is approximately double the actual slope.

Question the-st