The point (1;2) is on the line that is perpendicular to the line x+y-1=0. Determine the equation of the perpendicular line?

We know that 2 lines are perpendicular if the product of
their slopes is -1.

We'll put the equation of the given
line in the point slope form:

y =
mx+n

For this reason, we'll keep y to the left side and
we'll move the rest of terms to the right side:

y = -x +
1

Comparing, we'll get the slope of this line: m1 =
-1

The slope of perpendicular line is m2 =
-1/m1

m2 = -1/-1

m2 =
1

The equation of the perpendicular line, that has the
slope m2 = 1 and it passes through the point (1;2) is:

y -
2 = 1*(x - 1)

y - 2 = x - 1

x
- y - 1 + 2 = 0

x - y + 1 =
0

The equation of the perpendicular line
is:

x - y + 1 =
0