# Question Video: Comparing the Rates of Change of Two Given Linear Functions Mathematics • 8th Grade

Determine which of the given functions has a greater rate of change. [A] Function a [B] Function b

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### 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, weβ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 π¦ over the changes in π₯. We also write that as π¦ two minus π¦ one equals π₯ two minus π₯ one.

Starting with function a, weβll need to choose two points to be our π₯ one, π¦ one and our π₯ two, π¦ two. You can choose any two points on the chart. Iβm going to choose one, zero and two, two. Our first point, we label π₯ one, π¦ one. And our second point, we call π₯ two, π¦ two.

Now we plug this information into our formula. π¦ two equals two, π¦ 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 π¦ equals ππ₯ plus π, 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 represents the rate of change. Another word that we use here is the slope. What we do now is look at our equation, π¦ equals three π₯ plus five, and identify which value is in the π position. Here, the π 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.