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## Algebra (all content)

### Course: Algebra (all content)>Unit 13

Lesson 7: Direct and inverse variation

# Recognizing direct & inverse variation: table

Sal is given a table with a few values of the variables x and y, and determines whether the variables vary directly or inversely. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

• at about in the video. Can someone explain the difference between direct and joint? thanks
• Well...direct variation is y=kx, whereas in joint, it is y=kzx
• How are these concepts of direct, inverse, and joint variation used in everyday life?
• Direct variation occurs all the time - whenever you have item pricing. If macadamias are \$8 per pound, then cost and quantity of food are in a direct relationship. The more macadamias you want, the more you have to spend. `cost = 8 * pounds`.

Inverse relationships come up whenever you're splitting something. If you bought 10 pounds of macadamia nuts, and have unknown number of people coming over to eat it, the serving size that person eats is inverse to the number of people that come over. `serving = 10 / people`.

Joint variation is a combination of the two concepts. Instead of `serving = 10 / people`, you could write `serving = pounds / people`, where you've created a variable for pounds of food instead of it being a constant.
• Is there a video about joint variation? Because it would really help! Thanks.
• do you have a video on PARTIAL variation??
thanks
• Sal said that the direct relation means that when x increases y will also increase, but what if the constant is negative? It becomes inverse right?
• If the constant is negative and you increase x, then y will become more negative, so it's still a direct variation.
• if w varies directly with x, x varies inwersely with y, and y varies inversely with z what equation would show how w relates to z?

to get this i started with three equations w=kx, x=yc, and y=zb (note c and b are just versions of k) then i preformed subsitution until i got to one equation, hope this helps
• Does direct variation automatically indicate a linear function?
• Yes. Here is why:
The equation of a linear function is y=mx+b.
If b=0, then you get y=mx, the formula for direct variation.
• Is it conventional to write y= kx or x=ky?
• The convention is to write the dependent variable (the vertical axis) on the left by itself with all the terms containing the independent variable (the horizontal axis) on the right.
So, if y were a function of x, then x would be the independent variable and y would be the dependent variable. i.e. y = kx
• Could someone please explain in the video