Find the equation of a perpendicular line.

Question

Find the equation of the line perpendicular to y= 1/3x -5 and going through the point (1,4)?

Answer 1

Slope intercept form line equation is y = mx + b. where m = slope and b is y -intercept.

Slope = 1/3

If two lines are perpendicular, the slope of one line (m1) is equal to opposite reciprocal of second line slope (m2). so, m1 = -1/m2

Slope of the perpendicular line = -1/(1/3) = -3

y -intercept value (b) value can be found by replacing the x and y coordinate values in the equation with the given point (1, 4)

4 = -3 * 1 + b

4 = -3 + b

b = 7

The line equation is y = -3x + 7

The line equation is 3x + y - 7 = 0