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Line $a$ has a slope of $\frac{7}{5}$ . Line $b$ has a slope of $\frac{5}{7}$ . Are line $a$ and line $b$ parallel or perpendicular? $\newline$ Choices: $\newline$ (A) parallel $\newline$ (B) perpendicular $\newline$ (C) neither

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Slopes of parallel and perpendicular lines

Full solution

Q. Line

a

has a slope of

\frac{7}{5}

. Line

b

has a slope of

\frac{5}{7}

. Are line

a

and line

b

parallel or perpendicular?

\newline

Choices:

\newline

(A) parallel

\newline

(B) perpendicular

\newline

(C) neither

Line a slope: Line a slope: $\frac{7}{5}$ . Line b slope: $\frac{5}{7}$ . Parallel lines have the same slope, perpendicular lines have slopes that are negative reciprocals.
Line b slope: Check if slopes are negative reciprocals: $(\frac{7}{5}) \times (\frac{5}{7}) = \frac{35}{35} = 1$ . Negative reciprocal would be $-1$ .
Check slopes product: Since the product of the slopes is $1$ and not $-1$ , lines $a$ and $b$ are not perpendicular.
Lines not perpendicular: Since the slopes are not the same, lines $a$ and $b$ are not parallel.
Lines not parallel: Lines $a$ and $b$ are neither parallel nor perpendicular.

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