Question

The points (9,9) and (10,k) fall on a line with a slope of -1. What is the value of k?

Answer 1

The value of k is 8

Solution:

Given that, points (9, 9) and (10, k) fall on a line with a slope of -1

To find: value of "k"

The slope of a line with points
`(x_1, y_1)` and
`(x_2, y_2)` is given as:

`m=(y_(2)-y_(1))/(x_(2)-x_(1))`

Here given that,

slope = m = -1

`(x_1, y_1) = (9, 9)\\\\(x_2, y_2) = (10, k)`

Substitute the values in formula, and solve to get value of k

`m = (k-9)/(10-9)\\\\-1 = (k-9)/(10-9)\\\\-1 = (k-9)/(1)\\\\k-9 = -1\\\\k = -1+9\\\\k = 8`

Thus the value of k is 8