I do not understand what this question is asking and how to get the result for it:

Question

"Suppose we have a metal bar of length L0 metres at temperature T0 in degrees Celsius.When the bar is heated or cooled, the length of the bar changes. The amount that the length changes is proportional to the product of the temperature change and the original length of the bar L0. Let á be the proportionality constant of this change where the units for á is measured in m/m◦C (metres per metres degree Celsius). Find an expression for the length L of the metal bar as a function of the temperature T.Draw a sketch of the graph of this function, labelling the point where T = 0."

So far I have figured that you have to have these values of length and temperature proportional to each other so like when length increases, the temperature decreases and as length decreases the temperature increases. But I do not know how to write that and how to come about drawing the graph.

Answer 1

Well, let's see what they have said.
dL = k dT L0
so,
L = k*L0*T + C

Now you can plug in initial conditions or boundary conditions to determine k and C