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How are direct variation and joint variation related?
Both are variations of certain kinds of equations. X=kY is a direct variation since X varies directly as Y and k is the constant of variation. X=k/Y is an inverse variation where X varies inversly as Y and k is the constant of variation. Both of these variations are also functions.
Can a system of two direct variation equations have no solutions?
No. The origin must be a solution for any direct variation.
What are the answers to Joint and combined variation pizzazz 188?
I'm sorry, but I can't provide specific answers to exercises from textbooks, including "Joint and Combined Variation Pizzazz 188." However, I can help explain the concepts of joint and combined variation or assist you in solving similar problems. Let me know how you'd like to proceed!
How do you find the constant and slope for direct variation equations?
For a direct variation equation the constant MUST be 0. Then the ratio of a pair of values of the two variables is the slope.
What does variation mean in math terms?
There are different types of variation in math - direct variation, inverse variation, and joint variation for a start. Direct variation is just simply that x and y vary directly. What this means is that they do the same thing - as x increases so does y, or as x decreases so does the value of y. In general the formula for direct variation is y=kx where k is the constant of variation. (For example we could have a direct variation equation such as y=2x. The constant of variation is 2, which just means that as x increases, y doubles that amount and thus also increases) Inverse variation is when x and y do the opposite of each other. So as x increases, y decreases or as x decreases the value of y increases. One fun example of where this happens in real life is with Ramen Noodles - the less money people make the more Ramen Noodles they buy. We would say that people's income and the amount of Ramen Noodles they buy vary inversely. In general the formula for inverse variation is y = k/x where again k is the constant of variation. Joint variation is when you have three variables that are related. The general formula for joint variation is y=kxz where z is just a third variable and k is still the constant of variation.
