Find the real number m if the distance from the point(m, m+1) to the line 3x-4y-1=0 is 1.

We'll note the given point as A(m,
m+1).

We'll write the formula of the distance from a given
point to a given line:

d(A, line): |3*m - 4*(m+1) -
1|/sqrt[3^2 + (-4)^2]

But d(A, line) =
1

|3*m - 4*(m+1) - 1|/sqrt[3^2 + (-4)^2] =
1

(3*m - 4*(m+1) - 1)/sqrt(9+16) =
1

We'll multiply by sqrt 25 both
sides:

3m - 4m - 4 - 1 =
sqrt25

We'll combine like
terms:

-m - 5 = 5

We'll add 5
both sides:

-m = 10

m =
-10

The coordinates of the point A are: A(-10
, -9).