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What are parallel lines?

The blue and the green lines shown on this graph are parallel. Parallel lines extend forever in each direction, and they never touch or intersect each other. When parallel lines are represented using an equation, their slopes have identical values, but their \( y \)-intercepts have different values.

A detailed description of this image follows in the next paragraph.

Graph of two parallel lines. One line is blue. The other line is green.

Look at the images shown below. Each image represents a set of parallel lines. Study each one carefully and then click it to learn why the set can be described as parallel lines.

Graph of two parallel lines. Use enter key to open full-screen view.
Image captioned below. Use escape key to exit full screen view.

This graph contains a pair of parallel lines. You know they are parallel because they extend forever in each direction and they do not touch or intersect.

Train tracks that are parallel.. Use enter key to open full-screen view.
Image captioned below. Use escape key to exit full screen view.

These tracks are parallel. They do not touch or intersect as they extend in either direction.

Use enter key to open a description of the two equations in this image.

\( \Large y = \ \require{color}\colorbox{yellow}{$ - 2 $}x + 8 \)

\( \Large y + 3 = \ \require{color}\colorbox{yellow}{$ - 2 $}(x - 4) \)

These equations represent parallel lines because they have identical slope values. In each equation, \( m = - 2 \).

Each of these equations has a different \( y \)-intercept. The \( y \)-intercept of \( y = - 2x + 8 \) is \( (0,\ 8) \).

Rewriting \( y + 3 = - 2(x - 4) \) in slope-intercept form yields:

\( y + 3 = - 2(x - 4) \)

\( y + 3 = - 2x + 8 \)

\( y = - 2x + 5 \)

The \( y \)-intercept of this equation is \( (0,\ 5) \).

Question

Look at the graph shown. Are these lines parallel? Explain your answer.

A detailed description of this image follows in the next paragraph.

Graph of two intersecting lines.