Question

Christian just lit a new candle and then let it burn all the way down to nothing. The length of the candle remaining unburned, in inches, can be modeled by the equation L=6−t where t represents the number of hours since the candle was lit. What is the slope of the equation and what is its interpretation in the context of the problem?

Answer 1

Given:

The length of the candle remaining unburned, in inches, can be modeled by the equation

$L=6-t$

where, t represents the number of hours since the candle was lit.

To find:

The slope and its interpretation in the context of the problem.

Solution:

Slope intercept form of a linear function is

$y=mx+b$

where, m is slope and b is y-intercept or initial value.

We have,

$L=6-t$

It can be written as

$L=6+(-1)t$

The coefficient of t is -1. So, using slope intercept form the slope of this equation is -1.

Here, -1 means length of the candle remaining unburned is decreasing at the rate of 1 inch per hour.