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Video: Comparing the Rates of Change of Two Given Linear Functions

Kathryn Kingham

Determine which of the given functions has a greater rate of change. (a) Table (b) 𝑦 = 3𝑥 + 5

02:46

Video Transcript

Determine which of the given functions has a greater rate of change.

Before we can determine which function has the greater rate of change, we’ll need to find the rate of change for both, function a and function b. When working with functions, the rate of change equals the changes in 𝑦 over the changes in π‘₯. We also write that as 𝑦 two minus 𝑦 one equals π‘₯ two minus π‘₯ one.

Starting with function a, we’ll need to choose two points to be our π‘₯ one, 𝑦 one and our π‘₯ two, 𝑦 two. You can choose any two points on the chart. I’m going to choose one, zero and two, two. Our first point, we label π‘₯ one, 𝑦 one. And our second point, we call π‘₯ two, 𝑦 two.

Now we plug this information into our formula. 𝑦 two equals two, 𝑦 one equals zero, π‘₯ two equals two, π‘₯ one equals one. Two minus zero equals two. Two minus one equals one. We reduce that to two, and the rate of change of function a equals two.

Finding the rate of change of function b is actually a little bit easier. Function b is in the form 𝑦 equals π‘šπ‘₯ plus 𝑏, which is the equation form of a straight line. And this is good news for us. When an equation is in this form, the π‘š represents the rate of change. Another word that we use here is the slope. What we do now is look at our equation, 𝑦 equals three π‘₯ plus five, and identify which value is in the π‘š position. Here, the π‘š is three. The slope, or the rate of change, of function b equals three.

So we have the rate of change of function b equals three. The rate of change of function a equals two. Now we need to compare which is greater. Three is greater than two which means the rate of change of function b is greater than the rate of change for function a.