Write an equation for the line that is perpendicular to the given line and that passes though the given point: y=-1/3x+2:(4,2)

Answer 1

Any line has a general equation y = ax + b where a is the slope and b is the intercept. (Intercept is where it crosses the y axis).

To solve this problem, first we use the fact that this new line is perpendicular to the given line. This means that its slope is negative inverse of the given line, The negative inverse of -1/3 is simply 3. So that's my slope or a.

Second, we use the fact that it passes through the point (4, 2) which means:

y = ax + b ----> or 2 = 3 (4) + b This can be easily solved for b which gives us b = -10

So the line we are after has the equation: y = 3 x - 10

Let me know if you have any questions.

Answer 2

Use point-slope form

(y - 2) / (x - 4) = 3 slope of perpendicular is negartve reciprocal