Question

Find the equation (in terms of x) of the line through the points ( − 1 , − 1 ) and( 4 , − 4 )

Answer 1

`y = -(3)/(5)x -(8)/(5)`

Explanation:

Given

`(x_1,y_1) = (-1,-1)`

`(x_2,y_2) = (4,-4)`

Required

Determine the line equation

First, calculate the slope (m)

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

`m = (-4 - (-1))/(4 - (-1))`

`m = (-4 +1)/(4 +1)`

`m = (-3)/(5)`

`m = -(3)/(5)`

The equation is then calculated using:

`y - y_1 = m(x - x_1)`

This gives:

`y - (-1) = -(3)/(5)(x - (-1))`

`y + 1 = -(3)/(5)(x +1))`

Open bracket

`y + 1 = -(3)/(5)x -(3)/(5)`

Make y the subject

`y = -(3)/(5)x -(3)/(5)-1`

`y = -(3)/(5)x +(-3-5)/(5)`

`y = -(3)/(5)x +(-8)/(5)`

`y = -(3)/(5)x -(8)/(5)`