I have the following points and have asked to find the line of best fit equation.
(2001, 17.60) and (2002, 18.75)
I keep coming up with y = 1.15x - 2283.55
but the answer book shows y = 1.15x + 12
1) What am I doing wrong with my equation?
This problem is about the average cost of baseball tickets over the years, so the +12 makes more sense in the context of the question, but I just cannot come up with that answer with my calculator.
2) I would assume that the 12 represents the amount that the tickets are going up, on average, per year?
3) They say that the y-intercept is (0, 12) -- how does this even make sense? If the x is the year and the y is the cost, in 0 years the cost was $12? Please help me understand this!!
I'm going to correct myself on #2 above and say the slope, 1.15, is representing that on average the cost of the tickets is going up 15% per year?
I also get your equation. The only thing I can see is that 2283.55/12 = 190
So maybe they are talking about the average ticket cost since baseball was invented 190 years ago.
If tickets cost $12 in 1811, then the costs shown in your plot are the prices after rising for 190 years.
the 15% angle is a good idea. Of course, now you have to do an exponential curve fit. To turn that into a straight line, use the log of the cost, turning your points into (2001, 1.246) and (2002,1.273)
Then your equation is
log y = mx+b
1) It seems there might be a mistake in your calculation. Let's re-evaluate it to find the correct equation for the line of best fit.
The general equation of a line is y = mx + b, where m is the slope of the line and b is the y-intercept. To find the line of best fit, we need to determine the values of m and b.
Let's start by finding the slope:
m = (change in y) / (change in x) = (18.75 - 17.60) / (2002 - 2001) = 1.15 / 1 = 1.15.
Now, let's find the y-intercept by substituting one of the given points into the equation:
17.60 = 1.15 * 2001 + b
17.60 = 2301.15 + b
b = 17.60 - 2301.15
b = -2283.55.
Hence, the equation of the line of best fit should be y = 1.15x - 2283.55, which matches with your initial calculation.
2) The value of 12 in the answer book might represent the y-intercept or the starting point of ticket prices in a particular year. It can be interpreted as the cost of the tickets in the initial year of the data set. However, it does not necessarily indicate the average annual increase in ticket prices.
3) The statement that the y-intercept is (0, 12) means that at the year 0 in the data set (most likely a reference year rather than an actual year), the cost of tickets was $12. The x-axis is commonly used to represent the independent variable (in this case, the year), while the y-axis represents the dependent variable (the cost of tickets). In this specific context, it does not imply that the cost of tickets would reach $12 in zero years.
It's important to note that when interpreting mathematical models or equations, it's crucial to consider the context and make logical connections with the variables and values presented.