Question

How do you find the slope of the line that is perpendicular to the line through (1, 9) and (10, 3 and 1/2)?

Answer 1

`18/11`

Find the slope of the line by dividing the change in the y values by the change in the x values. Then take the negative inverse of the slope of the line.

Explanation:

The slope equals the change in `y` divided by the change in `x`, so

`y = 9 - 3 1/2 = 5 1/2`

`x = 1 - 10 = -9`

`"slope" = (5 1/2)/(-9)`

Multiply `5 1/2 xx 2 = 11`, then multiply `-9 xx 2 = - 18`, so the slope of the line is

`"slope" = - 11/18`

The negative inverse is `+ 18/11`

So the slope of the line that is perpendicular to the line is `+ 18/11`