Video: Determining Which of a Group of Functions Is Not Linear

Video Transcript

Which of the following equations represents a nonlinear function? In order to be a linear function, it must be in the form 𝑦 equals 𝑚𝑥 plus 𝑏, where 𝑚 is your slope and 𝑏 is your 𝑦-intercept.

Option A, we can use the distributive property. And it becomes 𝑦 equals five 𝑥 minus fifteen. This is in the 𝑦 equals 𝑚𝑥 plus 𝑏 form, so this is a linear function. Five is your slope and negative fifteen is your 𝑦-intercept. Right away, we can also see that option D is already in that linear form. 𝑦 equals five 𝑥 plus six, so five is the slope and six is the 𝑦-intercept. So now let’s look at B and C.

In order to be in the form 𝑦 equals 𝑚𝑥 plus 𝑏, 𝑦 must be isolated. It must be by itself. So nine and 𝑥 are both being multiplied to 𝑦, so we can divide both sides by nine and 𝑥, resulting in 𝑦 equals four over nine 𝑥. Now for a linear function, the 𝑥 needs to be on the numerator. If you look, 𝑦 equals 𝑚𝑥 plus 𝑏 that’s technically 𝑥 over one.

So right here what we have, we have 𝑦 equals four over nine 𝑥, but 𝑥 is on the denominator. That is not the same as 𝑥 being on the numerator, so B would represent a nonlinear function. Now just to double check C, we can rewrite this instead of 𝑥 over two. That’s the same as one half 𝑥, and there’s no 𝑦-intercept which means it’s just zero. So that would be 𝑦 equals one half 𝑥 plus zero. So that would also be linear. So again, option B is what would represent a nonlinear function.