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?
would a be 2001?
If they're sratring at
x = 1 -> Y1 = 1997 , then
x = 2 -> Y2 = 1998
then you can just count for a) and b)
In the formula y = mx + c, m is the slope and c is the y-intercept, which should answer a couple of them.
f) Once you've counted to 2018, just let x equal that year number; that'll let you work out y.
a) To determine the year represented by x = 4, we can substitute the value of x into the equation y = 0.15x + 0.79.
Plugging in x = 4:
y = 0.15(4) + 0.79
y = 0.6 + 0.79
y = 1.39
Therefore, the year represented by x = 4 is the year 1997 + 4 = 2001.
b) To find the x-value representing the year 2018, we need to determine the value of x when y = 2018. Rearranging the equation, we get:
2018 = 0.15x + 0.79
Subtracting 0.79 from both sides:
2018 - 0.79 = 0.15x
2017.21 = 0.15x
Dividing by 0.15:
x ≈ 13481.4
Therefore, the x-value representing the year 2018 is approximately 13481.4.
c) The slope of this equation represents the rate of change. In this case, the slope is 0.15. Thus, the rate of change for each year is an increase of 0.15 units.
d) The y-intercept represents the point where the line intersects the y-axis. In this equation, the y-intercept is 0.79.
e) The y-intercept represents the starting value of the average cost of gas. It indicates that in the first year of the study (x = 1), the estimated average cost of gas was $0.79.
f) To estimate the price of gasoline in the year 2018, we can substitute x = 13481.4 into the equation and solve for y.
y = 0.15(13481.4) + 0.79
y ≈ 2022.21
Therefore, assuming the growth trend continues, the estimated price of gasoline in the year 2018 would be approximately $2022.21.