In the 𝑥𝑦-plane, the point three, seven lies on the graph of 𝑦 equals five 𝑥 minus 𝑎. What is the value of 𝑎?
We’ve been given the coordinate pair three, seven. And when you’re given coordinates like this, the first number represents the 𝑥-coordinate and the second number represents the 𝑦-coordinate. This tells us that when 𝑥 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 𝑥 minus 𝑎. So we just need to substitute 𝑥 equals three and 𝑦 equal seven into that equation and solve for 𝑎. And that tells us that seven is equal to five times three minus 𝑎. And since five times three is 15, this means that seven is equal to 15 minus the value of 𝑎.
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 𝑎 is equal to eight. Now, an alternative approach to solving that equation for 𝑎 would be to spot the fact that we’ve got negative 𝑎 over on the right-hand side. So we want to know what positive 𝑎 is equal to. So I’m going to add 𝑎 to both sides of the equation. On the left-hand side, that gives me seven plus 𝑎. And on the right-hand side, if I’ve got 15 and then I take away 𝑎 and then add 𝑎, I just end up with 15.
Now because I want to know the value of 𝑎, I’m gonna subtract seven from both sides of this equation. Seven plus 𝑎 minus seven is just 𝑎. And 15 minus seven is eight. So I get the same answer. Now, our question asked us, what is the value of 𝑎? 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 𝑎 is equal to eight. Well, that would be 𝑦 equals five 𝑥 minus eight. But as we say, the question didn’t ask us that. So the answer is 𝑎 is equal to eight.