Question

What is the slope of any line perpendicular to the line passing through `(13,17)` and `(-1,-2)`?

Answer 1

See a solution process below:

Explanation:

First, we can find the slope of the line defined by the two points in the problem. 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)(-2) - color(blue)(17))/(color(red)(-1) - color(blue)(13)) = (-19)/-14 = 19/14`

One of the characteristics of perpendicular lines is their slopes are the negative inverse of each other. In other words, if the slope of one line is: `m`

Then the slope of the perpendicular line, let's call it `m_p`, is

`m_p = -1/m`

We can calculate the slope of a perpendicular line as:

`m_p = -1/(19/14) = -14/19`

Any line perpendicular to the line in the problem will have a slope of:

`m = -14/19`