WEBVTT
00:00:01.060 --> 00:00:08.020
For the following table, find the algebraic equation that shows the proportional relationship between π₯ and π¦.
00:00:10.150 --> 00:00:12.580
What is that mean β a proportional relationship?
00:00:14.380 --> 00:00:30.580
The variables in a function will change at a constant rate in a proportional relationship, and we use the formula π¦ equals ππ₯, where π is the constant rate that is changing the variables.
00:00:32.050 --> 00:00:40.330
And we can use the formula π¦ equals ππ₯ to help us figure out what the constant rate of change in this table is.
00:00:42.210 --> 00:00:46.670
Weβre asking here, what is happening to π₯ to give us π¦?
00:00:47.070 --> 00:00:50.390
What weβre multiplying our π₯ by to give π¦?
00:00:50.960 --> 00:00:55.140
And our first instance: π₯ equals six and π¦ equals 12.
00:00:55.620 --> 00:00:58.730
How did we go from six to 12?
00:01:00.040 --> 00:01:03.230
12 equals π times six.
00:01:04.670 --> 00:01:09.330
We recognize that our π, our constant rate of change, is two.
00:01:09.730 --> 00:01:15.930
Two times six equals 12; our constant rate of change equals two.
00:01:17.160 --> 00:01:21.450
Letβs check the other two points in our table to make sure thatβs true for them as well.
00:01:22.790 --> 00:01:24.810
Does seven times two equal 14?
00:01:25.820 --> 00:01:26.900
Yes, it does.
00:01:27.970 --> 00:01:30.340
Does eight times two equal 16?
00:01:31.520 --> 00:01:36.990
Yes, so all three of our points are following a constant rate of change of two.
00:01:38.630 --> 00:01:40.460
But our work here isnβt finished.
00:01:40.650 --> 00:01:45.600
Our question is asking, what is the algebraic equation that shows this?
00:01:46.630 --> 00:01:50.580
We plug in two to our proportional relationship formula.
00:01:51.140 --> 00:01:56.820
And then our algebraic equation becomes π¦ equals two times π₯.