Question

3x+4y=10 linear

Answer 1

yes it is linear

Answer 2

A linear equation is one where a small change in x produces a corresponding change in y which is the same no matter where you do it. Another way of looking at it is that the slope of the line described by the equation is constant. 3x + 4y = 10 is linear because it can be written 4y = 10 - 3x or y = 2.5 - 0.75x, which is just a straight line. If we had an x^2 term in there, it wouldn't be linear, and if you look at the graph of a parabola, you see that the same amount of displacement on the x axis can lead to wildly different changes in y depending on where you happen to be on the parabola.

Linear equations make the math so much more tractable that heroic efforts are made to use them, even though most physical matters are not completely linear when you look carefully enough.