Parallel and Perpendicular Slopes Explained
How the slopes of parallel and perpendicular lines relate — equal slopes, negative reciprocals, and worked examples.
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Frequently asked questions
What slopes do parallel lines have?
Equal slopes. Parallel lines have the same steepness and never intersect, differing only in their y-intercept.
What slopes do perpendicular lines have?
Negative reciprocals. If one slope is m, the perpendicular slope is −1⁄m, and the two multiply to −1.
How do I find a perpendicular slope?
Flip the slope into its reciprocal and change the sign. A slope of 3 gives −1⁄3; a slope of −1⁄4 gives 4.
How can I check if two lines are perpendicular?
Multiply their slopes. If the product is −1, the lines are perpendicular.
Are horizontal and vertical lines perpendicular?
Yes. A horizontal line (slope 0) and a vertical line (undefined slope) meet at right angles, though the reciprocal rule does not apply directly.
Can two lines with the same slope be perpendicular?
No. Equal slopes mean the lines are parallel (or the same line), never perpendicular.
Slopes of parallel and perpendicular lines
Two lines’ slopes reveal how they relate. Parallel lines never meet and have equal slopes. Perpendicular lines cross at a right angle, and their slopes are negative reciprocals of each other — multiply them and you get −1.
Parallel lines
If a line has slope 2, every line parallel to it also has slope 2; they differ only in their y-intercept. So y = 2x + 1 and y = 2x − 5 are parallel — same steepness, shifted up or down.
Perpendicular lines
To find a perpendicular slope, flip the fraction and change the sign. A slope of 3 (that is 3⁄1) becomes −1⁄3; a slope of −2⁄5 becomes 5⁄2. Check by multiplying: 3 × (−1⁄3) = −1, confirming the right angle.
One special case: a horizontal line (slope 0) is perpendicular to a vertical line (undefined slope). The negative-reciprocal rule breaks down here because you cannot take the reciprocal of zero, so these are handled separately.
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