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).