Linear vs. non-linear relationships

[TheJourney]

Ok, so I thought I understood the concept of linear relationships, but I don't.
I believed directly proportional meaning a linear relationship, but apparently it doesn't.

So the equation for the speed of a wave is: v = λf where v = velocity, λ = wavelength and f = frequency.

One of the question from BR Physics Section V states: "Which graph BEST represents the relationship between the wavelength and speed of waves emitted from a tuning fork, if the wave frequency is fixed?"
From the equation wavelength, λ, and speed, v, are directly proportional. So the graph is linear and the solution states that "the relationship is linear."

Another question from the same section states, "Which graph BEST represents the relationship between the frequency and wavelength of waves emitted from a stereo speaker, if the wave speed is fixed?"
From the equation wavelength, λ, and frequency, f, are inversely proportional. However, there are no exponents or inverse on either term, therefore I expected their relationship to be linear just inverse (one goes up, the other goes down). However, the solution marks the linear graph for this question as incorrect and states their "relationship is not linear."

If anyone can clarify that would be great.

The graph for the first question looks like this, as I expected:
http://www.mathsaccelerator.com/algebra/images/graph-motorbike.gif

The graph for the second question looks like this, just without ever reaching 0:
http://upload.wikimedia.org/wikipedia/en/4/47/Exponential_function_showing_time_constant.jpg

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[shahcoco]

Things that are indirectly proportional (ex. Inverse) are not linear. It has to be directly proportional, like your first example, to have a linear graph.

 

[inasensegone]

Admittedly I initially had some problems with graphs when I first started my review as well. I found it useful to test extremes. This is what I mean:

Take the equation at hand: v = λf. The question tells you that they want you to keep velocity constant and graph frequency (f) vs wavelength (λ). Plug in 100 for v as a test value.
If frequency = 100, then wavelength = 1.
f = 50, λ = 2.
f = 33.3, λ = 3.
f=25, λ = 4.
f =20, λ = 5

This isn't a linear change because the 2 are inversely proportional. They're on the same side of the equation and the other side is a constant, so when one goes up, the other goes down. You can see from the data points though, that the rate of change (slope) isn't constant, hence you get an asymptotic curve.

Once you do enough of these problems, you will intuitively know what the graphs begin to look like and how subtle changes shift the graphs.