What is the equation of a line passing through the point (a, b) and having a a slope of b?

1 Answer
Nov 14, 2016

#x-1/by=a-1#

Explanation:

In general the slope-point form of a line with slope #color(green)m# through a point #(color(red)a,color(blue)b)# is
#color(white)("XXX")y-color(blue)b=color(green)m(x-color(red)a)#

In this case, we are given a slope of #color(green)b#
So our equation becomes
#color(white)("XXX")y-color(blue)b=color(green)b(x-color(red)a)#

Dividing through by #b#
#color(white)("XXX")1/b y -1=x-a#

Then converting to standard form:
#color(white)("XXX")x-1/by= a-1#