The scatterplot below compares the average gasoline prices I Boston, per gallon, to the average gasoline prices across the United States, per gallon, during a one-year period from 2017 to 2018.

Of the following equations, whihc best modeles the data in the scatterplot ?

Options

A. `y =- 1.7848x+0.5842`
B. `y=1.7848x+1.5842`
C. `y=0.7848x+0.5842`
D. `y =- 0.7848x+0.5842`

Answer

C

Explanation

Notice that the answer choices involve very precise coefficients, which is a good indicator that logic is the best way to get to the correct answer. The slope of the line of best fit is positive, so eliminate (A) and (D), which have negatibve slopes. It is also important to note that the lower-left corner of the graph is not the origin, which means that the y-intercept needs to be extrapolated. With only two choices left, you can test only one of them. If the equation you test works, then it is correct. If the equation you test works, then it is correct. If the equation you test works, then it is correct. If the equation you test does not work, the other is correct. To test (B), choose one of the values for the scatterplot that is close to the line of best fit, for example (2.7,2.7). Pugging 2.7 in for x should mean that `y =2.7,` but with the equation in choice (B) you get:
`y = 1.7848(2.7)+1.5842`
`y = 4.81896+1.5842`
`y=6.40316`
This does not matcvh the coordinate point so (C) is corect.