Exercises: Parallel and Perpendicular Lines

Read each slope first -- directly from slope-intercept form, or with the $-\frac{A}{B}$ shortcut from standard form -- then compare.

Grade 10·17 problems·~30 min·Digital SAT Math·topic·sat-alg-lin2-parperp

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Warm-Up: Review What You Know

These review slope comparison.

Two distinct non-vertical lines are parallel when their slopes are:

Negative reciprocals of one another, so their product is $-1$ .

Equal to each other.

Opposite in sign but equal in absolute value.

Both equal to zero, since parallel lines cannot rise.

What is the negative reciprocal of $\frac{3}{4}$ ?

Extract each slope first, then compare.

Which line is parallel to $y = 4x - 7$ ?

$y = -\frac{1}{4}x + 2$ , since its slope is the negative reciprocal.

$y = -4x - 7$ , since it shares the same constant term.

$y = 4x + 1$

$y = \frac{1}{4}x - 7$ , since it shares the same constant term.

A line is perpendicular to $y = \frac{2}{5}x + 3$ . What is its slope?

What is the slope of the line $6x + 3y = 15$ ?

$6$ , read directly from the coefficient of $x$ .

$-2$

$2$ , the ratio of the two coefficients $\frac{6}{3}$ .

$3$ , read directly from the coefficient of $y$ .

Lines $p$ and $q$ have slopes $-\frac{3}{7}$ and $\frac{7}{3}$ . How are they related?

Parallel, because the same digits appear in both slopes.

Neither, because the slopes are neither equal nor opposite in sign.

Perpendicular

The same line, since one slope is the reciprocal of the other.

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