Question

What is the slope of any line perpendicular to the line passing through `(1,-7)` and `(3,-5)`?

Answer 1

See a solution process below:

Explanation:

First, we need to find the slope of the line passing through the two points. 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)(-5) - color(blue)(-7))/(color(red)(3) - color(blue)(1)) = (color(red)(-5) + color(blue)(7))/(color(red)(3) - color(blue)(1)) = 2/2 = 1`

Let us call the slope of a perpendicular line `m_p`

The formula for the slope of a perpendicular line is: `m_p = -1/m`

Substituting the slope we calculated gives us the slope of the perpendicular line as:

`m_p = -1/1 = -1`