A line has a slope of 3. A perpendicular line is drawn to this and it passes through the point (5, 4), what is the equation of the line.

2 Answers | Add Yours

justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The product of the slope of two perpendicular lines is equal to -1. If a line is perpendicular to a line with slope 3, the slope of the line is equal to `-1/3` .

As the line passes through the point (5,4), the equation of the line is `(y - 4)/(x - 5) = -1/3`

=> 3(y - 4) = 5 - x

=> 3y - 12 = 5 - x

=> x + 3y - 17 = 0

The required equation of the line is x + 3y - 17 = 0

Wiggin42's profile pic

Wiggin42 | Student, Undergraduate | (Level 2) Valedictorian

Posted on

Since the line has a slope of 3, the perpendicular line will have a slope of -1/3 since that is the negative reciprocal of 3. 

Plug this into the point slope formula: 

y - y1 = m(x - x1) where m is the slope and (x1, y1) is the point. 

y - 4 = (-1/3)(x - 5)

We’ve answered 318,996 questions. We can answer yours, too.

Ask a question