Question

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

Answer 1

`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`