1Cademy - Verifying that $$x = -2$$ and $$x = -5$$ are Parallel

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Parallel Lines

Example

Verifying that $x = -2$ and $x = -5$ are Parallel

To determine whether the lines $x = -2$ and $x = -5$ are parallel, attempt to use slopes and $y$ -intercepts.

Because neither equation contains the variable $y$ , they cannot be rewritten in slope-intercept form $y = mx + b$ . However, recognizing that each equation has the form $x = a$ identifies both as vertical lines.

The line $x = -2$ is a vertical line with $x$ -intercept $(-2, 0)$ .
The line $x = -5$ is a vertical line with $x$ -intercept $(-5, 0)$ .

Since their $x$ -intercepts are different ( $-2$ vs. $-5$ ), the two vertical lines are parallel.

This example illustrates the special case where the standard slope-comparison method does not apply because vertical lines have undefined slopes. Instead, parallelism for vertical lines is confirmed by checking that they have different $x$ -intercepts — each line occupies a distinct vertical position on the coordinate plane, so they never cross.

Updated 2026-04-21

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OpenStax Elementary Algebra

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