Question

The points (-1, -5) and (-3, x) lie on the same line. if the slope of the line is -1, what is the value of x?

Answer 1

x = - 3

Explanation:

calculate the slope m , between the 2 points using the slope formula , then equate to the given value of m = - 1

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

let (x₁, y₁ ) = (- 1, - 5 ) and (x₂, y₂ ) = (- 3, x )

substitute these values into the formula for m

m =
`(x-(-5))/(-3-(-1))` =
`(x+5)/(-3+1)` =
`(x+5)/(-2)`

now equate to m = - 1

`(x+5)/(-2)` = - 1 ( multiply both sides by - 2 )

x + 5 = 2 ( subtract 5 from both sides )

x = - 3