Parallel Lines
Two lines are parallel if their slopes are equal.
Two lines are parallel if the respective coefficients of x and y are proportional.
Two lines are parallel if their directional vectors are equal.
Two lines are parallel if the angle between them is 0º.
Examples
Calculate k so that the lines r ≡ x + 2y − 3 = 0 and s ≡ x − ky + 4 = 0, are parallel.
Determine the equation for the line parallel to r ≡ x + 2 y + 3 = 0 that passes through the point A = (3, 5).
Determine the equation for the line parallel to r ≡ 3x + 2y − 4 = 0 that passes through the point A = (2, 3).
3 · 2 + 2· 3 + k = 0 k = −12
3x + 2y − 12= 0
The line r ≡ 3x + ny − 7 = 0 passes through the point A = (3, 2) and is parallel to the line s ≡ mx + 2y − 13 = 0. Calculate the values of m and n.
