Question

Explaining a Solution
A table contains the ordered pairs (3, 42.25) and (5, 50.75). If the relationship in the table is linear, explain how to find the initial value.

Answer 1

A linear relation has form y = mx + b, where b is the initial value (y when x = 0).

1. Find the slope m = (change in y)/(change in x) = (50.75 − 42.25)/(5 − 3) = 8.5/2 = 4.25.
2. Use one point to solve for b: b = y − m x. Using (3, 42.25), b = 42.25 − 4.25·3 = 42.25 − 12.75 = 29.5.

So the initial value (y-intercept) is 29.5.