Question

How do you find the equation of the line which goes through the point (2,-1) and is tangent to the line given by the equation `2x-y=1`?

Answer 1

If `2x - y = 1`
then `y = 2x -1`
and the slope, `(dy)/(dx)`, is `2`

So, we are looking for an equation of a line going through `(2,-1)` with a slope of `2`.

Specifically, for any point (x,y) on the line
the slope between that point and `(2, -1)` must be `2`

`(y - (-1))/(x - 2) = 2`

`y + 1 = 2 (x -2)`

or (in more standard form)

`y = 2x - 5`

graph{y=2x-5 [-14.24, 14.24, -7.12, 7.12]}