# What was the original length of the candle if a candle is burning at a linear rate and the candle measures five inches two minutes after it was lit and it measures three inches eight minutes after it was lit?

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This is a problem where you are given two positions on a graph and are asked to find the equation of the line connecting them. In this case you are also being asked for the

The independent variable is time. We'll plot that on the x-axis. The dependent variable is the length of the candle. That will be the y-axis.

At two minutes the length of the candle is 5 inches.

At eight minutes the length of the candle is 3 inches.

We need to find the equation of a line which goes through the two points

The slope is easy to find

The intercept can be found from the point-slope formula by inserting one of the data points into the equation:

With a little algebra we can show that

And the length at time

A quick sanity check... since

What sort of candle do you think would burn at a rate of