I know what a linear graph looks like...I'm talking about if I need to identify the correct graph for a given problem.
For instance, the relationship between frequency and wavelength is non-linear, assuming velocity is constant. How do we know this?
On the other hand, relationship between wavelength and velocity is linear, if frequency is constant.
Is there a quick and easy way to discern the two?
I am not quite Einstein when it comes to math, what I do is keep a list in my head. If you remember Electromagnetic Speed c=3.0X10^8, c=f(lambda which stands for wavelength), so know that if you trying to solve for lambda or frequency (f), you divide the equation by the other variable.
Your best bet would be to rely on equation if you can't have the graph, so this is my simple way of remembering this:-
1) x=y (two variables on opposite sides of equal sign, but related in a way if you increase one, there is a concomitant increase in the other variable. ) Directly proportional, their graph would be linear.
2) x=y^2, x^2=y, x^# =y or y^# =x, either way know that these graphs aren't linear, since there isn't a proportional increase. What that means is as increases, so does the other but it isn't a concomitant increase.
3) x=1/y, 1/x=y, this implies a indirectly proportional relationship, so if you increase one you decrease another. An example is frequency and wavelength, falling under this relationship. Another way to picture this relationship is Electric Potential =1/r, "r" here stands for radius.
4) Finally 1/x^2=y or x=1/y^2, implies it's a indirectly proportional relationship, graph isn't linear, as one increase, the other exponentially decreases or vice versa. An example of this is any of the inverse square laws, gravitational force, electric force.
So let's take a look as how these look in graph, if you are given this:-
1. It's going to be a pretty much linear graph with a positive slope.
3. Linear graph with a negative slope.
2. Non linear graph, some form of positive slope
4. Non linear graph some form of negative slope.
One final thing, I have a problem with Math (as I have already mentioned), so what I do is go with equations, they have a clear cut relationships. So one thing you can try is when looking over particular equations, plug some numbers in and see what they yield, that should make the relationship of the variables abundantly clear.
Cheers!
