Line j has a slope of 4/9 . Line k has a slope of 5/3 .Are line j and line k parallel or perpendicular? Choices: (A)parallel (B)perpendicular (C)neither

Identify Slopes: Line j slope: 4/9. Line k slope: 5/3. To be parallel, slopes must be equal. To be perpendicular, slopes must be opposite reciprocals.Check for Parallel Lines: Check if slopes are equal: 4/9 ≠ 5/3, so not parallel.Check for Perpendicular Lines: Check if slopes are opposite reciprocals: Reciprocal of 4/9 is 9/4. Opposite of 9/4 is -9/4. But slope of line k is 5/3, not -9/4, so not perpendicular.Conclusion: Since slopes are neither equal nor opposite reciprocals, lines j and k are neither parallel nor perpendicular.

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Line $j$ has a slope of $\frac{4}{9}$ . Line $k$ has a slope of $\frac{5}{3}$ . Are line $j$ and line $k$ parallel or perpendicular? $\newline$ Choices: $\newline$ (A) parallel $\newline$ (B) perpendicular $\newline$ (C) neither

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Math Problems

Algebra 1

Slopes of parallel and perpendicular lines

Full solution

Q. Line

j

has a slope of

\frac{4}{9}

. Line

k

has a slope of

\frac{5}{3}

. Are line

j

and line

k

parallel or perpendicular?

\newline

Choices:

\newline

(A) parallel

\newline

(B) perpendicular

\newline

Identify Slopes: Line $j$ slope: $\frac{4}{9}$ . Line $k$ slope: $\frac{5}{3}$ . To be parallel, slopes must be equal. To be perpendicular, slopes must be opposite reciprocals.
Check for Parallel Lines: Check if slopes are equal: $\frac{4}{9} \neq \frac{5}{3}$ , so not parallel.
Check for Perpendicular Lines: Check if slopes are opposite reciprocals: Reciprocal of $\frac{4}{9}$ is $\frac{9}{4}$ . Opposite of $\frac{9}{4}$ is $-\frac{9}{4}$ . But slope of line $k$ is $\frac{5}{3}$ , not $-\frac{9}{4}$ , so not perpendicular.
Conclusion: Since slopes are neither equal nor opposite reciprocals, lines $j$ and $k$ are neither parallel nor perpendicular.