I'm having trouble trying to understand linear functions.
First, we recognize a function from a graph using vertical straight line, if it crosses two points, we say the graph does not represent a function.
if we use the vertical line method on y = mx + c if m equals or approaches to infinity, then y = mx + c does not represents a function, let alone represent a linear function.
Am i right or wrong in this situation ?
On
The general formula to represent a line in 2D space is: $Ax+By+C=0, A\in R, B\in R$($A$ and $B$ should not equal to $0$ simultaneously), and $y=mx+c$ is a restricted form that excludes the case $B=0$.
So, w.r.t your question, a vertical line is exactly the case that $B=0$, and $Ax+C=0, A\neq 0$ is a function of $y$, namely $x(y)=0$, which means that given any $y$, $x$ remains the same number $-\frac{C}{A}$. It can be understood in the same way with $y=c$.
And, when you let $m\to\infty$, you reach the limitation of the representation ability of this restricted form $y=mx+c$.
Well.. as the 'm' represents the slope of the line which is given by tan (angle of the line with the x-axis), so if the 'm' i.e. slope is equal to infinity therefore the tan of the angle will be infinity and since tan of 90 degree is infinity(actually its undefined but it approaches infinity at pi/2 radians so we can assume), thus your line will be perpendicular to the x axis.. for e.g. x = 5 can be such a line.