Question

Given A(2,3) and B(5,8), write an equation of a line parallel to AB containing the point P(-2,-4).

Answer 1

Let given points are

Slope of the AB line

We know that parallel lines slopes are equal.

Parallel line passes through P.

Equation of a line in point slope form is

Cross multiplication.

3y + 12 = 5x + 10

Subtract 12 from each side.

3y + 12 - 12 = 5x + 10 - 12

3y = 5x - 2

Divide each side by 3.

3y /3 = 5x /3 - 2/3

y  = 5x /3 - 2/3.

Requiered line equation y  = 5x /3 - 2/3.