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» » Rate of Change

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.



rate of change 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


rate of change



Make Sure...

that you really understand how to find the slope given two points! You will have trouble with real world problems if you don't understand this very important concept. If you need extra help, check out the Algebra Class E-course. You will find more examples on video with a lot of practice problems.

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.


finding rate of change



If you are having trouble figuring out this formula, watch the video for example #2 above.


youtube channel If you want to see this example on video, click here to visit my You Tube channel.


Let's look at another example.


rate of change
finding rate of change




And... one last example.


finding slope
finding rate of change





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.


Click here for a quick reference page that can be used when solving problems related to slope.


Click here to try a few practice problems on your own.



Take a look at the questions that other students have submitted:

question and answers

Finding slope for two points



To ask a question please visit my Math Forum.




Other Lessons You Might Like on Graphing Equations


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