This online Parallel Line Calculator finds the equation of the line that is parallel to a given line. You have to specify the parameters a and b of the original line y = ax + b as well as the coordinates of the point (x0,y0) through which the parallel line y = px + q passes. After clicking the ‘Calculate’ button you will get the parameters p and q and the graph of the parallel line.
Parallel Line Definition
Parallel lines are infinite lines that lie in the same plane and do not intersect at any point.
Let’s define two linear functions in the two-dimensional plane. The first function describes the first (original) line equation:
$$y = ax + b.$$
The second function will describe the parallel line equation:
$$y = px + q.$$
The parameters \(a\) and \(p\) are the slopes of these two lines. It is easy to show that the slope of the parallel line \(p\) is equal to the slope of the original line \(a\):
$$p = a.$$
If we know that the parallel line passes through the point \((x_0,y_0)\) on the plane, then we can easily find the parameter \(q\):
$$q = y_0 \ – \ a x_0.$$
Plugging the known parameters \(a\), \(b\), \(x_0\), \(y_0\) to our Parallel Line Calculator you will get instantly the parallel line parameters \(p\) and \(q\). You will get also a graph that shows the original line, the parallel line, and the point through which the parallel line passes.
Related calculators
Check out our other math calculators such as Perpendicular Line Calculator or Linear Interpolation Calculator.