the average price of a movie ticket has increased linearly over the years, rising from $5.39 in 2000 to $7.89 in 2010.

Question

Using these two data points, find a linear function, f(x)=mx+b, that models the data. Let x represent the number of years since 2000. Then use this function to estimate the average price of a movie ticket in 2005 and 2015.

Answer 1

Tawny,

you can map this data on the Cartesian plane as follows:

The x-axis shows the year and the y-axis shows the price in $. based on this you can map the data as (2000,5.39) and (2010,7.89) where the first number is the x-coordinate and the second is y- coordinate. so your line should pass both these points. You can use the following formula to find the equation of the line having two points:

Y-y1=((y2-y1)/(x2-x1))×(X-x1)

you can select any of the points mentioned above as (x1,y1) or (x2,y2). I pick x1 = 2000, y1 = 5.39, x2 = 2010 , y2 = 7.89. using the formula:

Y-5.39 = ((7.89-5.39)/(2010-2000))× (X-2000)

Simplifying:

Y-5.39 = 0.25×(X-2000) --> Y=0.25X-494.61

Hope this helps!