### Video Transcript

Which of the following equations represents a nonlinear function? In order to be a linear function, it must be in the form π¦ equals ππ₯ plus π, where π is your slope and π is your π¦-intercept.

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

In order to be in the form π¦ equals ππ₯ plus π, π¦ must be isolated. It must be by itself. So nine and π₯ are both being multiplied to π¦, so we can divide both sides by nine and π₯, resulting in π¦ equals four over nine π₯. Now for a linear function, the π₯ needs to be on the numerator. If you look, π¦ equals ππ₯ plus π thatβs technically π₯ over one.

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