Question

What is the slope of any line perpendicular to the line passing through `(2,15)` and `(10,21)`?

Answer 1

See a solution process below:

Explanation:

First, we need to find the slope of the line going through 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)(21) - color(blue)(15))/(color(red)(10) - color(blue)(2)) = 6/8 = 3/4`

Let's call the slope of the perpendicular line: `m_p`

The slope of a perpendicular can be found using the formula:

`m_p = -1/m` (This is the negative inverse)

Substituting gives:

`m_p = -1/(3/4) = -4/3`