Question

A line passes through the points (-6,4) and (-2,2). Which is the equation of the line?

Answer 1

The answer is y= -1/2x + 1

Answer 2

The equation of the line is
`y=(-1)/(2)x+1`

Explanation:

1. The equation of the line that passes through two points can be expresed as:

`(y-y_1)/(x-x_1)=(y_2-y_1)/(x_2-x_1)` (Eq.1)

where
`x_(1)`,
`x_(2)`,
`y_(1)` and
`y_(2)` are the given points.

2. Name the points:

`x_(1)`=-6

`x_(2)`=-2

`y_(1)`=4

`y_(2)`=2

3. Replace the points in the Eq.1:

`(y-4)/(x-(-6))=(2-4)/(-2-(-6))`

`(y-4)/(x+6)=(2-4)/(-2+6)`

`(y-4)/(x+6)=(-2)/(4)`

`(4(y-4))/(x+6)=-2`

`4(y-4)=-2(x+6)`

`4y-16=-2x-12`

`4y=-2x-12+16`

`4y=-2x+4`

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

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

`y=(-1)/(2)x+1`