Question

A candle burned at a steady rate. After 32 minutes, the candle was 11.2 inches tall. Eighteen minutes later, it was 10.75 inches tall. Use an equation in point-slope form to determine the height of the candle after 3 hours. Round the answer to the tenth place if necessary.

Answer 1

Let
x = time, minutes
y = length, inches

When x = 32 min, y = 11.2 in
When x = 32+18 = 50, y = 10.75 in
Assume that a linear relatioship exists between x and y.

In table form, the given data is
x, min: 32 50
y, in: 11.2 10.75

The slope is
m = (10.75 - 11.2)/(50 - 32) = -0.025

In point-slope form, the required equation is

`(y-10.75)/(x-50)=-0.025 \\\\ y-10.75 = -0.025(x-10.75)`

When x = 3 hours = 180 minutes, obtain
y - 10.75 = -0.025*(180 - 50) = -3.25
y = -3.25 + 10.75 = 7.5 in

Answer: 7.5 inches