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#?

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Answer 1 · 2015-02-22T13:12:53

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]}