Question

What is the equation of the line that is

PARALLEL to line AB
and passes through the point (2, -1)

Answer 1

`y = m_(AB)(X-2)-1`

Explanation:

When two lines are parallel means that their slopes are equal. Therefore the line AB will have same slope to a parallel second line,
`m_(AB) = m_(2)`.

To obtain the slope from the line AB, we need two points, so the general equation will be:

`m_(AB) = (y_(B) -y_(A)  )/(x_(B)-x_(A)  )`

The typical equation of a line is written as y = mx + b

The second line will pass through point (2, -1), so we can substitute:

y2 = mX2 + b

-1 =
`-1=m_(AB) (2)+b`(2) + b

then the interception is
`b=-m_(AB) -1`

Now to obtain a general equation for the second parallel line will be:

y =
`m_(AB)` X + b

y =
`m_(AB)` X -
`m_(AB)`(2)-1

Finally we get:

y =
`m_(AB)` (x-2)-1