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

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

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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).

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