Find the equation of a line parallel to the y-axis, that goes through the point $(\pi,0)$ I have been trying to do this problem and I am very confused.
I know the gradient is infinity when any line is parallel to the y-axis, therefore, $y = \infty \cdot x + c$, right ($y = mx + c$ being the general equation a straight line)?
We know $y = 0$, therefore $0 = \infty \cdot \pi + c$ and so $c = -\infty \cdot \pi$. Therefore, $y = \infty \cdot x - \infty \cdot \pi$. And therefore $y = 0$ which would seem to check-out?
But, the answer I have been given (by my teacher) says $x = \pi$. Please can somebody explain how you come to this answer?

Is this in $\mathbb{R}^2$? If so, the equation $y=mx+b$ will not help you, as the slope of any line parallel to the $y$-axis is undefined. Instead, a vertical line (parallel to $y$-axis) has the equation $x=a$, where $a$ is the $x$-intercept of the line. This should clarify the (correct) answer provided by your teacher. 
