Identifying equations of linear graphs

0:00- [Instructor] We're asked which equation best represents the relationship between x and y in the graph. Pause this video and try that before we do it together. All right, now let's do this together. And what I can do is let's just look at some points on that graph and see if we can eliminate some of these equations, or even identify exactly which one it is.

0:22So one that I always like is when one of the variables, especially x is equal to zero. So when x is equal to zero, it looks like the value of the graph here is y is equal to negative six. So we're at zero, negative six. Just off of that, we can eliminate a few of these.

0:39Can you figure out which ones those are? Well, for choice A right here, if x is zero then y is zero. So this one won't work. And that's also true for choice D. If x is zero, y is zero. Both A and D describe proportional relationships where y is equal to some constant times x and you're not adding or subtracting some other constant.

1:00If it was a proportional relationship, having trouble saying that, then this line would go through the origin. It clearly doesn't, so we can rule out these two proportional relationships. So now we're left with B and C, and if x equals zero in either of these cases, it does look like y indeed would be equal to negative six.

1:20So let's try another point. Let's see if we can identify something else interesting here. So it looks like, I'm trying to find something that looks pretty clean, at least to my eyes. So this point right over here, it looks like when x is six, y is four. And we're just eyeballing, and it looks like it's exactly at x equals six, y is equal to four, but as long as it's close then that means that that graph might be there, we're just eyeballing it wrong, but let's see what these would actually result in.

1:54So in choice B right over here, let me do this some place else, in choice B right over here, when x is equal to six, we have, we're gonna have to do it up here, we're gonna have 3/5 times six minus six, which is equal to, let's see, three times six is 18/5. 18/5 minus six, see, 18/5 is three and 3/5, am I doing that right?

2:2518/5 is three and 3/5. And then if we were to subtract six from it, you would get a negative number. You wouldn't get a four right over there. So I'm going to rule this one out. And so just process of elimination, it looks like choice C should work. But let's verify that.

2:43So if I do the math on choice C, if we were to say 5/3 times six minus six, this is the same thing as five times six is 30 divided by three is 10. This is 10 minus six, which is indeed equal to four. So choice C all checks out.