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

In the π‘₯𝑦-plane, the point (3, 7) lies on the graph of 𝑦 = 5π‘₯ βˆ’ π‘Ž. What is the value of π‘Ž?

02:08

Video Transcript

In the π‘₯𝑦-plane, the point three, seven lies on the graph of 𝑦 equals five π‘₯ minus π‘Ž. What is the value of π‘Ž?

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

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‘Ž is equal to eight. Now, an alternative approach to solving that equation for π‘Ž would be to spot the fact that we’ve got negative π‘Ž over on the right-hand side. So we want to know what positive π‘Ž is equal to. So I’m going to add π‘Ž to both sides of the equation. On the left-hand side, that gives me seven plus π‘Ž. And on the right-hand side, if I’ve got 15 and then I take away π‘Ž and then add π‘Ž, I just end up with 15.

Now because I want to know the value of π‘Ž, I’m gonna subtract seven from both sides of this equation. Seven plus π‘Ž minus seven is just π‘Ž. And 15 minus seven is eight. So I get the same answer. Now, our question asked us, what is the value of π‘Ž? So in fact, our work is done. But while we’re here, let’s just think about the equation of this line, now that we know that π‘Ž is equal to eight. Well, that would be 𝑦 equals five π‘₯ minus eight. But as we say, the question didn’t ask us that. So the answer is π‘Ž is equal to eight.

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