Rate of Change
Connecting Slope to Real Life

Why do we need to find the slope of a line?

The slope of a line tells us how something changes over time. If we find the slope we can find the rate of change over that period.

Take a look at the following graph.

This graph shows how John's savings account balance has changed over the course of a year. We can see that he opened his account with $300 and by the end of the first month he had saved $100. By the end of the 12 month time span, John had $1500 in his savings account.

John may want to analyze his finances a little more and figure out about how much he was saving per month. This is called the rate of change per month.

By finding the slope of the line, we would be calculating the rate of change.

We can't count the rise over the run like we did in the calculating slope lesson because our units on the x and y axis are not the same. In most real life problems, your units will not be the same on the x and y axis. So, we need another method!

We will need to use a formula for finding slope given two points.

Finding Slope Given Two Points

Now, let's look at a few real life problems.

Real Life Problems

Let's go back and look at John's Savings Account graph again.

Let's look at another example.

And... one last example.

The three examples above demonstrated three different ways that a rate of change problem may be presented. Just remember, that rate of change is a way of asking for the slope in a real world problem.

Real life problems are a little more challenging, but hopefully you now have a better understanding.

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