SOLUTION: The linear equation y = 0.15x + 0.79 represents an estimate of the average cost of gas for year x starting in 1997. The year 1997 would be represented by x = 1, for example, as it

Question 146241: The linear equation y = 0.15x + 0.79 represents an estimate of the average cost of gas for year x starting in 1997. The year 1997 would be represented by x = 1, for example, as it is the first year in the study. Similarly, 2005 would be year 9, or x = 9.
a) What year would be represented by x = 4?
b) What x-value represents the year 2018?
c) What is the slope (or rate of change) of this equation?
d) What is the y-intercept?
e) What does the y-intercept represent?
f) Assuming this growth trend continues, what will the price of gasoline be in the year 2018? How did you arrive at your answer?

Answer by solver91311(12126) (Show Source):
You can put this solution on YOUR website!
a. if 1997 is year 1, then 1998 is year 2 (x = 2), then ...

b. 2018 minus 1997 plus 1. (Subtract 1997 from your result in part a to see why you have to add 1)

c. The equation is in slope-intercept form , so the slope is the coefficient on x.

d. The y-intercept is the ordered pair where x = 0 and y is the value you get when x = 0. Substitute 0 for x in the equation and do the arithmetic to get the y-coordinate of the y-intercept.

e. In this case the y-intercept represents the average cost of gasoline in year 0, or one year before year 1 which was 1997. (actually, this equation represents the average cost per gallon of gasoline adjusted for 2007 dollars. If it was actual price, the y-intercept value would have been about a buck and a quarter.)

f. (second part of the question). Substitute the value of x you derived in part b of the question for x in the equation. Do the arithmetic.

Super-Double-Plus-Extra Credit How good is this mathematical model at predicting the price of gasoline into the future? Hint: Solve the equation for , then go down to the corner gas station and compare your answer with the prices on their sign.