If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Main content

## 8th grade

### Course: 8th grade>Unit 3

Lesson 13: 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.

## Want to join the conversation?

• ur voice makes me sleepy sal
(16 votes)
• 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?
(5 votes)
• So it's not a liner if it doesn't show a line
(5 votes)
• 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.
(5 votes)
• 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?
(5 votes)
• Wait so it's linear? I'm hopelessly confused. What about the big jump from 5 to 8?
(3 votes)
• You'd divide the change in y with the change in x to find the constant.
(2 votes)
• So is the problem linear or non-linear? It's non-linear right? Because it did not make a straight line?
(3 votes)
• 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.
(4 votes)
• I need help with linear bc I in 5th grade
(2 votes)
• at the end of the video why did he add 9/2 + 15/2?
(2 votes)
• 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.
(1 vote)
• Im confused. How would you solve an Indirect Variation if it was something like Y= X (Exponent of 2) +3?
(1 vote)
• What's a Indirect Variation? Also your username is hopelessly complicated. How do you remember that?
(3 votes)
• How go I find the missing coordinate of an equation
(2 votes)

## Video transcript

Find the missing value to make the table represent a linear equation. So let's see this table right over here. So when x is equal to 1, y is 3/2. When x is 2, y is equal to 3. So let's see what happened. When x increased by 1, what did y do? Well looks like y increased by 3 and 1/2 is the same thing as 1 and 1/2. So to go from 1 and 1/2 to 3, it increased by 1 and 1/2, or you could say it increased by 3/2. You could say that 3 is the same thing as 6/2, 6/2 minus 3/2 is another 3/2. All right. Now when we go from 2 to 3, we're increasing by 1 again in x. And what are we doing in y? So we're going from 3, which is the same thing as 6/2 to 9/2. So once again, we are increasing by 3/2. So in order for this to be a linear equation or a linear relationship, every time we increase by 1 in the x direction, we need to increase by 3/2. If we increase by 2, we need to increase by 2 times 3/2. So what are we doing over here on this fourth term on the table? Well we're increasing. We're going from 3 to 8 so we are increasing by 5. So if we're increasing x by 5, then we need to increase y by 5 times 3/2 or 15 over 2. So that's the amount that we have to increase y by. If we started at 9/2 and we're going to increase by 15/2, so it's going to be 9/2 plus 15/2, this is how much we increment by. Remember, we increment 3/2 every time x moves 1. This time, x moved 5. So we're incrementing by 15/2, or you could say we're incrementing by 3/2 five times. But this is going to be equal to 9 plus 15 is 24 over 2 which is equal to 12. And so in the box, we could write 12, and we are done.