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

Which of the following equations represents a nonlinear function? [A] 𝑦 = 5(π‘₯ βˆ’ 3) [B] 9π‘₯𝑦 = 4 [C] 𝑦 = π‘₯/2 [D] 𝑦 = 5π‘₯ + 6

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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 π‘šπ‘₯ plus 𝑏, where π‘š is your slope and 𝑏 is your 𝑦-intercept.

Option A, we can use the distributive property. And it becomes 𝑦 equals five π‘₯ minus fifteen. This is in the 𝑦 equals π‘šπ‘₯ 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 π‘₯ 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 π‘šπ‘₯ plus 𝑏, 𝑦 must be isolated. It must be by itself. So nine and π‘₯ are both being multiplied to 𝑦, so we can divide both sides by nine and π‘₯, resulting in 𝑦 equals four over nine π‘₯. Now for a linear function, the π‘₯ needs to be on the numerator. If you look, 𝑦 equals π‘šπ‘₯ plus 𝑏 that’s technically π‘₯ over one.

So right here what we have, we have 𝑦 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. That’s the same as one half π‘₯, and there’s no 𝑦-intercept which means it’s just zero. So that would be 𝑦 equals one half π‘₯ plus zero. So that would also be linear. So again, option B is what would represent a nonlinear function.

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