What are parallel lines?

Parallel lines are defined as any set of two or more lines that when extended to infinity, would never cross paths. In other words, the slopes of these lines are either equal or opposite.

For example, two lines both with the slope 3/4 would be parallel, but also a line with the slope 3/4 and the slope -3/-4 would also be parallel since even though they are headed in opposite directions, they would never cross paths when extended to infinity.

Parallel Line Formula

The following formulas are used to calculate a parallel line.

m1 = m2

  • Where m1 is the slope of the first line
  • m2 is the slope of the second line

b = y2-m2*x2

  • Where b is the y-intercept in the parallel line
  • y2 is any y coordinate on the parallel line
  • X2 is any x coordinate on the parallel line

From these two equations, the slope-intercept form of the parallel line can be found and would equal:

y=m2*x + b

Finding Parallel Lines on a Graph

Two determine if two lines on a graph are parallel, first, find two coordinate points on each of the lines. Using those coordinate points, calculate the slope of each line. If those slopes are equal, then the lines are found to be parallel.

How to calculate a parallel line?

How to calculate a parallel line?

  1. First, determine the slope of the original line.

    Measure or calculate the slope of the original line. For this example, the original slope is found to be 4/1 = 4.

  2. Next, determine a coordinate point along a parallel line.

    In theory, this could be any point in space, but usually, it is given in the problem. For this example, the point given is X = 5 and Y = 3.

  3. Finally, calculate the equations of the parallel line.

    Using the formulas above, determine the parallel lines slope and y-intercept to come up with an equation.
    m1 = m2 = 5
    b = y2-m2*x2
    b= 3-(3*5)
    b = -12
    So, the final equation of the line would be:
    y = 4x -12

Related Calculators

Parallel Line Calculator

Enter the slope-intercept form of the first equation, and a coordinate point the second line passes through to calculate the equation of the second line.

parallel line calculator
parallel line formula