Equation Of A LineYou are currentlynot logged in Click here to log in 


If $y$ is 0 when $x$ is 0, that means we have:
In this case, $k$ is the ratio of changes.
In general, when $x=0$ the vaue of $y$ will not necessarily be $0.$ As a result, a more general form is:
If there is a point, $(x_0,y_0)$ that the line goes through, that means that when $x=x_0$ we must have $y=y_0.$ As a result, we have this form:
Using algebra to rearrange that equation, we have:
This is now in the same form as $y~=~kx+c.$
The constant $k$ in these equations is the "slope" of the line, and often the letter $m$ is used to represent the slope, rather than $k.$
In the sense of "Linear Algebra" a function $f$ is said to be "linear" if it satisfies the following:
Linear functions don't need to be just from $\mathbb{R}$ to $\mathbb{R}$ or $\mathbb{C}$ to $\mathbb{C}$ but can be from any set to any set, provided it has suitable concepts of addition and multiplication  such a set forms a vector space. In this way we can then start to represent linear functions by matrices. This is why "Linear Algebra" is really the study of matrices, and matrix multiplication.
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