Write Linear Equations Review

Question

Suppose a one year subscription to a magazine costs $12.99 and a 3 year subscription costs $25.98. The cost and length of the subscription are related. Write an equation to model the cost of a subscription for any period of time. How much should a 5 year subscription cost?

Answer 1

So for this problem, since it states the cost and length of the subscription are related, you can use the two subscription costs as data (or coordinate) points.

1. 1 year = 12.99, 3 year = 25.98; so (1,12.99), (3, 25.98) use these points to calculate the average rate of change (or the slope (m)).
2. (y - y₁)/(x - x₁) = m so, (25.98-12.99)/(3 - 1) = 6.495, this is the slope, m
3. y = 6.495(x) + b now just pick one of the points and put in the x and y values to solve for b
4. 12.99 = 6.495(1) + b solve for b and you discover it also = 6.495 = b
5. so y = 6.495(x) + 6.495 is the equation of the line, to answer their question, just pop in x=5 for the 5 years subscription cost
6. y = 6.495(5) + 6.495
7. y = $38.97

Does this make sense to you?