I really don't get direct variation and I took a test on it and bombed it but now I can correct it so if anyone can just explain it to me I'd be really grateful. :)
Generally, direct variation means that as one of the variables assumes increasing positive values the other variable has increasing positive values. The ommon example is
Direct Variation: y=kx where k is a positive number. That equation represents the set of lines through the origin with positive slope. You can verify that
y=mx+b with m>0 means x and y are directly related too. The counterpart to this is
Indirect Variation: y=k/x. When x assumes increasing positive values y has decreasing positive values. I think some texts/authors will state that x and y are inversely related in this situation too. The equation
y=k/x + c defines a set of hyperbolas, but you probably haven't covered these yet.
It needs to be pointed out that there's a fairly wide range of terminology and examples used to teach the concept of direct/indirect variation, so be sure to read your text carefully. We could point out for instance that a line with a negative slope has variables that are inversely related, but for the most part we're only concerned with positive values, not negative ones.
The importance of the concept and the reason for looking at only positive values is connected to the study of scientific formulas (this is a general statement too). If we look at the formula
distance = rate*time then you can verify that distance and rate are directly related: the faster you go, the further you travel in a fixed time period. Simple common sense, right?
By comparison, you might encounter a formula stating the relation of gravitational attracton between two objects of large mass. I think it looks something like
F=k*m*M/d^2 where F is the force of attraction, k is a special constant, m and M are the mass of the objects and d is the distance between the objects. (Don't worry if you haven't seen this formula, it's just an example.) In this formula the force varies directly with the mass of the objects (more mass = more attraction) and varies inversely with the distance (actually the square of the distance) between the objects. (The farther apart they are, the less the attractive force.) This formula isn't as obvious as the simple example for direct variation, but it is derived in physics.
If you have specific questions please post them and we'll try to help explain the concept more.
My question relates to the teaching of these concepts. I understand the concepts but am having problems deciding when to insert them in the curriculum. Would you suggest teaching these prior to teaching linear equations, during or after. When are they generally taught in algebra?
can i have more example about direct linear variation? cause i don't understand it.
k=5/4x
I would like to know the answer for k=5/4x.
I would like to know the answer for k=5/4x.
g~h and g=56 when h=4
i find this topic very hard to comprehend its not u it is my understanding skills
i find this topic very hard to comprehend its not u it is my understanding skills