Question

Which point below would you use with the point (-2,-5) to get a line with a slope of -1?

A. (4,1)
B. (1.4)
C. (-6, 1)
D. (-1,-6)

Answer 1

(D): (-1,-6)

Explanation:

Given

`(x_1,y_1) = (-2,-5)`

`m = -1`

Required

Find
`(x_2,y_2)`

Slope (m) is calculated using:

`m = (y_2 -y_1)/(x_2 - x_1)`

Substitute values for m, x1 and x2

`-1 = (y_2 -(-5))/(x_2 - (-2))`

`-1 = (y_2 +5)/(x_2 +2)`

Cross Multiply:

`-1(x_2 +2) = y_2 +5`

`-x_2 -2 = y_2 +5`

Make y the subject

`y_2 = -x_2 - 2 - 5`

`y_2 = -x_2 - 7`

Only (D): (-1,-6) satisfy this condition:

Substitute -1 for x2 and -6 for y2.

`-6 = -(-1) - 7`

`-6 = 1- 7`

`-6 =- 6`

Hence:

(D): (-1,-6) is true