Question

What is an equation of the line that passes through the points (0, -4) and (-4, 6)?

Put your answer in fully reduced form.

Answer 1

The equation of the line is.

`y=-(5)/(2)x-4`

Explanation:

Given:

The given points are (0, -4) and (-4, 6)

The equation of the line passing through the points
`(x_(1),y_(1))` and
`(x_(2),y_(2))` is.

`(x-x_(1))/(x_(2)-x_(1))=(y-y_(1))/(y_(2)-y_(1))`

Thus, the equation of the line that passes through the points (0, -4) and (-4, 6) is

`(x-0)/((-4)-0)=(y-(-4))/(6-(-4))`

`(x)/(-4)=(y+4)/(6+4)`

`-(x)/(4)=(y+4)/(10)`

`-(10x)/(4)=y+4`

`-10x=4(y+4)`

`-10x=4y+16`

`4y=-10x-16`

The above equation is divided by 2 both sides.

`2y=-5x-8`

`y=-(5)/(2)x-4`

Therefore, the equation of the line that passes through the points (0, -4) and (-4, 6) is
`y=-(5)/(2)x-4`