Question

What is the equation of the line that is
PARALLEL to line AB
and passes through the point (2, -1)

Answer 1

Answer:

$y = m_{AB}(X-2)-1$

Step-by-step 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:

$m_{AB} = \frac{y_{B} -y_{A}  }{x_{B}-x_{A}  }$

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