Linear Equation word problem (Below)

Question

A $100,000 life insurance policy for males age 39 costs $12.28. For males aged 54, the policy costs $15.58. Find a linear function P(x) that expresses the price P of the life insurance policy in terms of age x.

Answer 1

Age is like the "x" and policy cost is like the "y" in "y = mx + b" (linear function).

We are given two points as (x, y) values which are (39, 12.28) and (54, 15.58). We can use the slope equation to get "m":

So m = (15.58 - 12.28)/((54 - 39) = 0.22

Then we can use the point-slope form of a line, which is y - y₁ = m(x - x₁) to get the equation. I will use (39, 12.28) as my (x₁, y₁):

y - 12.28 = 0.22(x - 39)

y - 12.28 = 0.22x - 8.58

y = 0.22x + 3.7

Now, we can put it in function notation:

P(x) = 0.22x + 3.7