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Line $j$ has a slope of $\frac{8}{9}$ . Line $k$ has a slope of $\frac{9}{8}$ . Are line $j$ and line $k$ 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

j

has a slope of

\frac{8}{9}

. Line

k

has a slope of

\frac{9}{8}

. Are line

j

and line

k

parallel or perpendicular?

\newline

Choices:

\newline

(A) parallel

\newline

(B) perpendicular

\newline

(C) neither

Check slopes for parallel/perpendicular: Line $j$ slope: $\frac{8}{9}$ . Line $k$ slope: $\frac{9}{8}$ . Check if slopes are same for parallel or opposite reciprocals for perpendicular.
Slope comparison for parallel lines: Slope of line $j$ is the reciprocal of slope of line $k$ . $\frac{8}{9}$ is not equal to $\frac{9}{8}$ , so they're not parallel.
Opposite reciprocal comparison: Opposite reciprocal of $\frac{8}{9}$ would be $-\frac{9}{8}$ . $\newline$ Slope of line $k$ is $\frac{9}{8}$ , which is not the opposite reciprocal of $\frac{8}{9}$ .
Final determination: Since slopes are neither equal nor opposite reciprocals, lines $j$ and $k$ are neither parallel nor perpendicular.

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