Determine the line ty = 3x - 2 when it is perpendicular to the line y = 1 - x.

If the 2 given lines are perpendicular, then the product
of the values of their slopes is -1.

The given
equations are  y = 1 - x and ty = 3x - 2, so we'll have to put the equation ty = 3x -
2 in the standard from, which is y = mx+n.

Since y is
isolated to the left side, we'll just have to divide by t both
sides:

y = (3/t)*x - (2/t)

The
other line is:

y = -x+1

So,
the slope can be easily determined as m1 = -1.

That means
that the slope of the line y = (3/t)*x - (2/t) has the
value:

m1*m2 = -1

-1*m2 =
-1

-1*(3/t) =
-1

t =
3

The line, perpendicular to
the line y = 1 - x, is now determined, having as equation: y = x -
(2/3).