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
\[ b = y2 - m2 \cdot x2 \]
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:
\[ y = m2 \cdot x + b \]
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.
To 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.