### 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, weβll 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, weβll
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. Iβm 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
ππ₯ 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.