00:01
So in this question, we've been told that q is a linear function of p, which means that we can write the relationship between q and p as a straight line equation.
00:10
So q equals m times p plus c, where m is the gradient and c is the y -intercept.
00:17
Now we can find out what m and c are by using the points that we've been given.
00:22
So for instance, we know that when q is 6, p is minus 6.
00:26
So we get 6 equals minus 6m plus c.
00:30
And we know that when q is minus 18, p is 2.
00:33
So we get minus 18 equals 2m plus c.
00:37
So let's call this equation 1 and this one equation 2.
00:40
And we're going to do equation 2 minus equation 1.
00:46
So if we do that, we get minus 18 minus 6.
00:49
So we get minus 24 equals 2m minus minus 6m gives us 8m and the c's cancel.
00:57
So that means that m is minus 3.
01:01
Okay, and now we can just put this into equation 1.
01:06
So we get 6 equals minus 6 times minus 3, which is 18 plus c.
01:13
So that means that c is 6 minus 18, which is minus 12.
01:19
So our equation is q equals minus 3p minus 12.
01:29
Okay, so that's our equation.
01:31
So let's work out which of the following is true.
01:34
So a, q could be proportional to p.
01:37
Well, that's only true if the y -intercept is 0...