Question

An important postulate in geometry states: "Through Point P, there is only one line parallel to ". What is the equation of line l, parallel to that passes through Point X?
A ( -10,8) B(2,3) X(-5,10)

This is on a graph and I have to show steps and I am stumped

Answer 1

At first we will find the slope of the line that passes through the points A and B

A ( -10,8), B(2,3)
slope = (Δy)/(Δx) = (3-8)/(2-(-10)) = -5/12

the require line is parallel to the line passes through the points A and B
∴ the slope of the line that passes through Point X = -5/12
and have a general form
   y = m x + c
where m is the slope and c is constant
the constant can be calculated by substituting with the point x (-5,10) in the equation of general form
∴ 10 = (-5/12)*-5 + c
   c = 10 - 25/12 = 95/12
∴ y = (-5/12)x +95/12  ⇒⇒⇒⇒ multiplying the equation by 12

∴ 12y = -5x +95