# 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.

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Expert Answers

justaguide | Certified Educator

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**

Student Comments

Wiggin42 | Student

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)