Notes for Lesson 4-1 – Using Graphs to Relate Two Quantities

4-1.1 – Analyzing a graph

We can use graphs to show and analyze what is happening between two variables or actions. For example if we look at the following graph.

This graph shows the relationship between time and the amount of air in a balloon. As you can see the volume of air in the balloon increases every time you blow into it, and stays the same when you pause to breathe. During the 4th time you blow into the balloon it pops and the volume immediately becomes zero again.

Describe what could be happening in the following two graphs:

4-1.2 – Matching a table and a graph

Tables and graphs can both be used to show a relationship between variables. We just use graphs to visually display in the information because it is easier to display what happens.

a.

b.

4-1.3 – Sketching a graph

We also need to be able to sketch a graph ourselves for a situation so we can show others what we are meaning.For example:

Or –

Create a graph to show the amount of water in a bath tub as you take a bath.

Water level

Time

You are swinging on a swing and you get higher with each swing, then you slow down until you come to a stop.