Given a point on the line and a parallel line is enough information to determine the equation of the line.

The equation of the line is:

y-y1 = m (x-x1)

We are given the point passes through the line (x1, y1) then we can substitute into the equation.

Now to detrmine the slop (m) we look at the parallel line.

the slope of any parallel lines are equal.

For example.

The line passes through ( 1,2) and parallel to y= 3x-2

y-y1- m (x-x1)

==> y-2 = m(x-1)

Now the slope should be equal to the slope of the line y= 3x -2

The slope then is m= 3

==> y-2 = 3 (x-1)

==> y-2 = 3x -3

**==> y= 3x -1**