Question

The scatterplot below shows the relationship between the number of gallons of gasoline in the tanks of 14 cars, and the maximum number of miles the cars can be driven on the given amount of gasoline.

Gasoline
A graph has gallons in gas tank on the x-axis and maximum miles on the y-axis. A line goes through points (9, 280) and (12, 360).

Based on the data collected, which combination of gallons in the gas tank and maximum number of miles seems most likely to be possible?


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Answer 1

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B.9 gallons in the gas tank and 280 miles.

From the given figure we see that the line of best fit passes through the point (13,400) and (17,520)

We know that the equation of a line passing through two point (a,b) and (c,d) is calculated by using the formula

y - b = d-b/c-a x (x-a)

Here we have:

(a,b)=(13,400) and (c,d)=(17,520)

Hence, the equation of line of best fit is: y - 400 = 520 - 400/17-3 x (x - 13)

y-400=120/4 x (x-13)

y=400=30x(x-13)

y-400=30x-390

y=30x-390+400

If u want to check your answers

0 gallons in the gas tank and 20 miles

when x=0 we have:

y=10≠20

Hence, option: A is incorrect.

B)

9 gallons in the gas tank and 280 miles .

when x=9 we have:

y=30×9+10

y=280

Hence, option: B is correct.

C)

11 gallons in the gas tank and 360 miles

when x=11; we have:

y=30×11+10

y=340≠360

Hence, option: C is incorrect.

D)

19 gallons in the gas tank and 520 miles

when x=19; we have:

y=30×19+10

y=580≠520

Hence, option: D is incorrect.