Slope of 2 lines

An SAT Math micro-topic under Graphs of linear equations and functions (Algebra). Free to read — no account needed.

The slopes of two lines tell you how the lines are related.
Equal slopes mean the lines are parallel.
Slopes that multiply to −1-1 mean the lines are perpendicular.
parallel_perpendicular.png
The figure shows both cases.
Parallel lines rise at the same rate, so they stay the same distance apart.
Perpendicular lines meet at a right angle, and their slopes multiply to −1-1.
To get a perpendicular slope, flip the fraction and change the sign.
The perpendicular slope to 43\frac{4}{3} is −34-\frac{3}{4}.
Check: 43×(−34)=−1\frac{4}{3} \times \left(-\frac{3}{4}\right) = -1.
A parallel line just copies the slope.
A line parallel to y=3x−7y = 3x - 7 also has slope 33.
The intercept can differ, but the slope must match.

Worked examples

A line has slope 33. What is the slope of a line perpendicular to it?
Flip 33 to 13\frac{1}{3} and negate it.
So the perpendicular slope is −13-\frac{1}{3}.
The line y=3x−7y = 3x - 7 is given. What is the slope of any line parallel to it?
Parallel lines have equal slopes.
So the parallel slope is 33.
A radius has slope 43\frac{4}{3}. What is the slope of the tangent line, which is perpendicular to it?
Flip 43\frac{4}{3} to 34\frac{3}{4} and negate it.
So the tangent slope is −34-\frac{3}{4}.

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