Gross domestic box office is the amount of money made by movies in theaters in the United States. In the year 1998 the total gross domestic box office was 6.9 billion. In 2008 the total gross domestic box office was 9.6 billion.
Find a linear function modeling this relationship. Let M(t) represent the gross domestic box office (in billions) t years after 1990.
Becky
I do not like this problem for pre-algebra students. There are standard techniques for solving this kind of problem, which are usually taught
after algebra. If you have quoted the problem accurately, it is asking you to find an answer without either the data or technique to do it the best way. Nevertheless, let's do the best we can.
I am using y=mx+b and subtracting y2 from y1 and x2 from x1 to get my slope. I am just unsure how the 1990 fits in I got my formula which I believe to be M(t)=0.27t-532.56 just not sure if I plug the 1990 in for t or what I am to do with it?
But you do not tell us what x and y are. Always name your variables in writing. It helps avoid confusion and aids communication. The problem suggests using t for time. Is x or y your substitute for t? (In general, I like to use letters that help me remember what variables the letters represent. So I suggest using t for time, measured in years after 1990, and d for dollars in billions.) So you are looking for an equation of the form
d = b + m(t). Why that form rather than t = b + m(d)?
\(\displaystyle \dfrac{d - 9.6}{t - (2008 - 1990)} = \dfrac{9.6 - 6.9}{(2008 - 1990) - (1998 - 1990)} \implies \dfrac{d - 9.6}{t - 18} = \dfrac{9.6 - 6.9}{2008 - 1990 - 1998 + 1990} = \dfrac{2.7}{10}\implies\)
\(\displaystyle 10(d - 9.6) = 2.7(t - 18) \implies 10d - 96.0 = 2.7t - 48.6 \implies 10d = 47.4 + 2.7t \implies d = 4.74 + 0.27t.\)
Let's check.
\(\displaystyle 4.74 + 0.27 * 8 = 4.74 + 2.16 = 6.90.\)
CHECKS
\(\displaystyle 4.74 + 0.27 * 18 = 4.74 + 4.86 = 9.60.\)
CHECKS
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