Question

a plot is shown relating the number of vehicles using alternative fuels to the number of years since 1992.
vehicles using alternative fuels
number of vehicles
0 200,000 300,000 400,000 500,000
number of years since 1992
0 2 4 6 8 10
$y = 18,891x + 275,763$
based on the equation of the line of best fit for the data, which statement is a valid conclusion?
(a) the average number of vehicles using alternative fuels in the united states from 1992 to 1999 was approximately 18,891.
(b) the increase in the number of vehicles using alternative fuels in the united states every year varied from approximately 18,891 to approximately 275,763.
(c) the number of vehicles using alternative fuels in the united states increased from approximately 18,891 in 1992 to approximately 275,763 in 1999.
(d) the number of vehicles using alternative fuels in the united states increased from approximately 275,763 in 1992 by approximately 18,891 every year up to 1999.

Explanation:

Step1: Analyze the line equation

The line of best fit is $y = 18891x + 275763$, where $x$ = years since 1992, $y$ = number of vehicles.

Step2: Check each option

• a: 1999 is $x=7$: $y=18891×7 + 275763=132237+275763=408000≠18891$. False.
• b: The equation’s slope is positive (18891), so $y$ increases with $x$. The statement says "varied from...", but the line shows a consistent increase. False.
• c: 1992 is $x=0$: $y=275763$; 1999 is $x=7$: $y=408000$. 408000≠18891. False.
• d: Slope=18891 means $y$ increases by ~18891 per $x$ (year). True.

Answer:

d. The number of vehicles using alternative fuels in the United States increased from approximately 275,763 in 1992 by approximately 18,891 every year up to 1999.