To find the equation for a line of best fit, we need to calculate the slope and y-intercept using the given data points.
Let's calculate the slope (m) using the formula:
m = (Σxy - (Σx)(Σy) / n(Σx²) - (Σx)²)
Σxy = (0)(26.40) + (2)(27.20) + (4)(29.70) + (6)(29.30) + (8)(32.20) + (10)(37.80) = 691.60
Σx = 0 + 2 + 4 + 6 + 8 + 10 = 30
Σy = 26.40 + 27.20 + 29.70 + 29.30 + 32.20 + 37.80 = 182.60
Σx² = (0²) + (2²) + (4²) + (6²) + (8²) + (10²) = 220
n = 6
m = (691.60 - (30)(182.60) / (6)(220) - (30)²
m = (691.60 - 5478) / (1320 - 900)
m = -4786.40 / 420
m = -11.39
Now, let's calculate the y-intercept (b) using the formula:
b = (Σy - m(Σx)) / n
b = (182.60 - (-11.39)(30)) / 6
b = (182.60 + 341.70) / 6
b = 524.30 / 6
b = 87.38
Therefore, the equation for a line of best fit is:
y = -11.39x + 87.38
To find the expected cost for a tank of gas in 2019, we need to substitute x = 2019 - 1998 = 21 into the equation:
y = -11.39(21) + 87.38
y = -239.19 + 87.38
y = -151.81
Since a negative cost does not make sense, we can assume that the cost for a tank of gas in the year 2019 would be $0.
You research the average cost of a tank of gasoline for a certain type of car for several recent years to look for trends. The table shows your data. What is the equation for a line of best fit? How much would you expect to pay for a tank of gas in the year 2019? Let x be the number of years after 1998.
Year:1998,2000,2002,2004,2006,2008
Average cost for one tank:$26.40,$27.20,$29.70,$29.30,$32.20,$37.80
answers:
y=1.02x+25.32;$46.74
y=26.40x+1.006:$58.92
y=26.40x+1.006:$47.52
1.006x+26.40:$47.52
1 answer
1 answer