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Course: Pre-algebra>Unit 14

Lesson 6: Linear and nonlinear functions

Linear & nonlinear functions: missing value

Learn to find the missing value in a table to make sure it represents a linear equation. Created by Sal Khan.

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• ur voice makes me sleepy sal
• In the Linear and nonlinear functions exercise, there is a type of question which displays an equation not in linear format and asks if the given equation can be expressed as a linear equation. Here's a link to a screenshot of an example: http://imgur.com/UC1j1su

I understand that because of the square (in some versions it's a square root) somehow, this precludes linear expression, but I don't understand the given proofs.

Here they prove it's not on a line by deriving three points, (0, -4)(-1, 1)(3, 5). I see (0, -4) comes from assuming -4 is the y-intercept, but where do the other two coordinates come from?
• So it's not a liner if it doesn't show a line
• In this example, isn't it more logical to just take "x = 2" and "y = 3" then multiply it by 4? That way "x = 8" (2 * 4 = 8) and "y = 12" (3 * 4 = 12.)
This is the method I always use, and I don't understand why it has to be made so much more complicated.
• Is there any way to tell if something is a linear function without making a graph? If the problem is 'Is y+9x a linear function?', is there a way to do it without a graph?
• So is the problem linear or non-linear? It's non-linear right? Because it did not make a straight line?
• It did make a straight line so it is linear. If Sal went and added the missing x-axis points 4, 5, 6, and 7, the y-axis points would be 6, 15/2, 9, and 21/2. Even though there was a jump from 3 to 8, if you were to graph it, the line would have a slope of 3/2.
• Ppl who is looking at this message then good luck and love to ya. <3
• Wait so it's linear? I'm hopelessly confused. What about the big jump from 5 to 8?
• You'd divide the change in y with the change in x to find the constant.
(1 vote)
• Wouldn't this table be non-linear since since the change in x and y wasn't constant? For example the change in x being +1, +1, and then +5
Or is it constant since the change in y also increased by 5 at the same time as x?
• You can't determine whether the points give a linear or non-linear graph just from the x values. You'll need to see how the y values change in response to a change in x values. So, see how as x increases by 1, y increases by 3/2. So, if x increases by 5, y must increase by 15/2 for the points to represent a linear equation (See that the whole purpose of the problem is to make the points part of a line)
• at the end of the video why did he add 9/2 + 15/2?
• For every increase of x by one, y was increasing by 3/2.

Since x increased by 5 in the table (from 3 to 8), the y would increase by 5 times 3/2. That is equal to 15/2.

The last value of y was 9/2, so he added 15/2 to that. It was a little tricky since the x side of the table jumped by 5.