Question

What is the slope of any line perpendicular to the line passing through `(3,7)` and `(18,11)`?

Answer 1

See a solution process below:

Explanation:

The slope can be found by using the formula: `m = (color(red)(y_2) - color(blue)(y_1))/(color(red)(x_2) - color(blue)(x_1))`

Where `m` is the slope and (`color(blue)(x_1, y_1)`) and (`color(red)(x_2, y_2)`) are the two points on the line.

Substituting the values from the points in the problem gives:

`m = (color(red)(11) - color(blue)(7))/(color(red)(18) - color(blue)(3)) = 4/15`

Let's call the slope of a perpendicular line: `color(blue)(m_p)`

The slope of a line perpendicular to a line with slope `color(red)(m)` is the negative inverse, or:

`color(blue)(m_p) = -1/color(red)(m)`

Substituting the slope for the line in the problem gives:

`color(blue)(m_p) = (-1)/color(red)(4/15) = -15/4`