Question

Line L has equation 2x - 3y = 5.
Line M passes through the point (3, -10) and is parallel to line L.
Determine the equation for line M.

Answer 1

For two lines to be parallel, They must have same SLOPE.

Slope of Line L :

2x - 3y = 5

2x + 5 = 3y

2/3x + 5/3 = y

This is in the form of y = mx + c, such that m = 2/3 ( this is the slope).

Since, Line L is parallel to Line M, Their slopes are equal,

So, slope of line M = 2/3

which implies, y = 2/3x + c.

Given, Line M passes through ( 3, - 10)
So,
-10 = 2/3 ( 3) + c
-10 = 2 + c
-12 = c.

Therefore, Equation of Line M ; y = 2/3x + 12, in other words
3y = 2x +36
2x - 3y = - 36