Equation of line passing through a point parallel to a given line

Question

I have the point $(2,-5)$ and an equation $y-4 = 2x$ which is a straight line. I want to make another equation from the $(2,-5)$ that is parallel to $y-4 = 2x$ and you can only do this by making the gradients the same or if they are both vertical lines. So I thought the easiest way was to make $(2,-5)$ a vertical line but I wasn't quite sure how to form it. I know that $x=k$ so would the vertical line equation in this case just be $x = 2$?

Answer 1

To first define what the vertical line equation is, it the equation $x=k$, with $a$ being the x-intercept and $k$ being some number. The way the setup should be is by plugging in the intersecting point of $(2,-5)$ into the equation by plugging in the x-intercept into the vertical line equation, and you get out $2=k$. Hence that $x=k$, $x=2=k$. Which concludes that the final equation is $x=2$.