Question

A direct variation function contains the points (-9, -3) and (-12, -4). Which equation represents the function?

Answer 1

=3y - x =0

Explanation:

`(y - y1)/(x - x1) = m`

Therefore the gradient ( m ) is not given

from the question point =(-9,-3) and (-12,-4).

Gradient (m) =

`(y2 - y1)/(x2 - x1) \\ = ( - 4 - ( - 3))/( - 12 - ( - 9)) \\ = ( - 4 + 3)/( - 12 + 9) \\ = ( - 1)/( - 3) \\ = (1)/(3)`

therefore m = 1/3.

The equation

`= (y - y1)/(x - x1) = m \\ (y - ( - 3))/(x - ( - 9)) = (1)/(3) \\ (y + 3)/(x + 9) = (1)/(3) \\ 3(y + 3) = 1(x + 9) \\ 3y + 9 = x + 9 \\ 3y = x + 9 - 9 \\ 3y = x + 0 \\ 3y - x = 0`

therefore the equation of the line = 3y-x=0