# Video: Using Knowledge of Coordinates to Find a Missing Value in a Linear Equation

In the π₯π¦-plane, the point (3, 7) lies on the graph of π¦ = 5π₯ β π. What is the value of π?

02:08

### Video Transcript

In the π₯π¦-plane, the point three, seven lies on the graph of π¦ equals five π₯ minus π. What is the value of π?

Weβve been given the coordinate pair three, seven. And when youβre given coordinates like this, the first number represents the π₯-coordinate and the second number represents the π¦-coordinate. This tells us that when π₯ equals three, then π¦ equals seven. And if that coordinate pair lies on this graph, it means that those coordinates satisfy the equation π¦ equals five π₯ minus π. So we just need to substitute π₯ equals three and π¦ equal seven into that equation and solve for π. And that tells us that seven is equal to five times three minus π. And since five times three is 15, this means that seven is equal to 15 minus the value of π.

And to solve this equation, I need to think, what do I need to subtract from 15 in order to get the answer seven? Well, 15 minus eight is seven. So π is equal to eight. Now, an alternative approach to solving that equation for π would be to spot the fact that weβve got negative π over on the right-hand side. So we want to know what positive π is equal to. So Iβm going to add π to both sides of the equation. On the left-hand side, that gives me seven plus π. And on the right-hand side, if Iβve got 15 and then I take away π and then add π, I just end up with 15.

Now because I want to know the value of π, Iβm gonna subtract seven from both sides of this equation. Seven plus π minus seven is just π. And 15 minus seven is eight. So I get the same answer. Now, our question asked us, what is the value of π? So in fact, our work is done. But while weβre here, letβs just think about the equation of this line, now that we know that π is equal to eight. Well, that would be π¦ equals five π₯ minus eight. But as we say, the question didnβt ask us that. So the answer is π is equal to eight.