` (##KPL_SAT_PRD_PLS_C09_E01_004_Q01.png" width="80%">
The scaterplot abouve shows data collected each year after the British Parlimament enacted a mandatory seat belt law and line of beast fit to the data. Which of the following equations best represents the trend of the data shown in the figure ?

Options

A. `y = 0.4x+25`
B. `y = 1.8x+15`
C. `y=2.1x+35`
D. `y=2.6x+25`

Answer

D

Explanation

A line that "represents the tread of the data" is another way of refereing to the line of best fit, which is linear in this diagram. Use the y-intercept and slope of the line of best fit to eliminate the choices. Start by finding the y-intercept. For this graph, it's about 25, so eliminate (B) and (C ). To choose between (A) and (D) find the approximate slope using two points that lie on (or very close to) the line of best fit. Use the y-intercept, (0,25), as one of the points to save time (it's easy to subtract 0) and estimate the second, such as (21, 80), Then, use the slope formula to find the slope:
` m = ( y _(2) -y_(1))/(x _(2) -x_(1)) = (80 -25)/(21-0) =(55)/(21) =2.62`
The results is very close to the slope is (D), making it the correct answer.