# How to Solve Relationships Among Functions

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Solving relationships among functions will require you to pay close attention to your given variables. Solve relationships among functions with help from an experienced mathematics educator in this free video clip.

Part of the Video Series: Math Lessons & Tips
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## Video Transcript

Hi, my name is Marija, and today I'm going to show you how to solve relationships among functions. So you can be given a function in a variety of different ways and I'm going to be giving it to you in a table today. So we're going to say our X values are 2, 3 and 4 and our Y values will be 5, 7 and 9. So we are trying to figure out what is the relationship, how do I get from X to Y? So what we are trying to figure out is our equation Y equals MX plus B and fill in our M, our slope and our B which is our Y intercept. So the first thing that you are going to do is pick two out of the three or however many points that you are given to find the slope, the M, and we're going to find that by doing the change in Y over the change in X. So the change in Y is found by subtracting 5 from 7. So when we do that we get 2 and then change in X we're going to go in the same order we have 3 minus 2 to get 1 which reduces to 2. So that means that our M value is going to be 2. We are multiplying the X by 2. In addition to that we're going to have to add or subtract some numbers. So now to find out what that other number is we're going to pick either one of these ordered pairs and substitute the X and the Y back into the equation. So if I pick the first ordered pair, the 5 is my Y so I'm going to substitute that in for Y, the M I just found that it was 2 so I'm writing a 2. The X is also 2 because it's right here in the table and then I'm just writing plus B because I don't know the B yet. Now I simplify and I get 5 equals 4 plus B and when I subtract 4 on both sides, I get B equals 1. So now that I have my M as 2 and my B as 1, I can go ahead and write the full function equation which is Y equals 2X plus 1, so that means that whatever X I'm giving, if I multiply by 2 and then add 1 to that product I will get the Y value.

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