Parallel Lines (Linear Functions)

Lines in a plane

Two lines in the plane are parallel if they do not intersect.

If two straight lines $g,hg,h$ are given in the line equation $g:y=m_{1}x+t_{1}h:y=m_{2}x+t_{2}g:\; y\; =\; m\_1x+t\_1\backslash \backslash h:\; y\; =\; m\_2x\; +\; t\_2$ then they are parallel exactly when $m_1=m_{2}m\_1\; =\; m\_2$, i.e. when the slopes of the two straight lines match.

You can try this out on this applet, where you can change the slope ($mm$) and intercept ($tt$) with the sliders.

Two parallel straight lines

The two pairs of short lines in the middle denote the parallelism

Lines in spaces

Two straight lines in space are parallel if they lie in a common plane and do not intersect. They are therefore parallel to each other in this plane.