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 represent the year 20018?
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?
A.Yr = 1997 + (x-1)
Yr = 1997 + (4-1) = 2000.
B. X = (2018-1997) + 1 = 22.
C. Y = 0.15x + 0.79.
m = 0.15.
D. Y-int. = 0.79.
E.The cost of gas before 1997.
F. C = 0.15*22 + 0.79 = $4.09.
A) To determine what year would be represented by x=4, we need to interpret the relationship given in the problem. In this case, x represents the number of years since 1997. Since 1997 is the first year of the study, we can assume that x=1 corresponds to 1997, x=2 corresponds to 1998, and so on. Therefore, x=4 would represent the year 1997 + 4 = 2001.
B) To find the x-value that represents the year 2018, we can again use the relationship that x represents the number of years since 1997. To determine the number of years from 1997 to 2018, we subtract 1997 from 2018, resulting in 2018 - 1997 = 21. Therefore, the x-value that represents the year 2018 is x=21.
C) The slope, or rate of change, of the linear equation is the coefficient that multiplies the x-variable. In this case, the coefficient of x is 0.15. Therefore, the slope of this equation is 0.15.
D) The y-intercept is the constant term in the equation, which is 0.79 in this case.
E) The y-intercept represents the value of y when x is equal to 0. In this context, it means that when x=0 (which corresponds to the starting year of 1997), the average cost of gas is 0.79 (whatever unit is used for the average cost of gas).
F) To determine the price of gasoline in the year 2018, we can substitute the x-value of 21 into the given equation.
y = 0.15x + 0.79
y = 0.15(21) + 0.79
y = 3.15 + 0.79
y = 3.94
Therefore, in the year 2018, the estimated average cost of gas would be $3.94 (assuming the linear equation accurately represents the trend).