Straight line equation is linear or not? I read somewhere that for the linearity the equation should pass through the origin in this regard the equation of straight line y=mx+c is linear or not?
 A: You are confusing terminology. The equation $$y = mx + c$$ (assuming that $x,y$ are variables and $m,c$ are constants) is a linear equation in $x$ and $y$. However, if $c$ is non-zero, then we would say that the line does not represent a vector space, as it does not pass through the origin. 
Here is some information on linear equations.
Here is some information on vector spaces.
A: There are two different uses of the word linear:


*

*Behaving as a polynomial of degree 1, i.e. $mx+c$, as opposed to quadratic, cubic, &c.

*Satisfies a functional equation, in particular,
$$ f(ax+by) = af(x)+bf(y), $$
for every $x$, $y$, $a$ and $b$ (where $x$ and $y$ might be vectors, for example, but $a$ and $b$ are real or complex numbers [not the most general case, but sufficient]).
The second is a subset of the first for real-valued functions of the type you're asking about: if $f(x)=mx+c$, then
$$ f(ax+by)-af(x)-bf(y) = m(ax+by)+c-a(mx+c)-b(my+c) = (1-a-b)c, $$
which is only zero if $c$ is zero, i.e. the graph of $y=f(x)$ passes through the origin.
