Line d has a slope of 4/7 . Line e has a slope of 3/2 .Are line d and line e parallel or perpendicular? Choices: (A)parallel (B)perpendicular (C)neither

Check slopes for parallel: Line d slope: 4/7. Line e slope: 3/2. To be parallel, slopes must be equal. To be perpendicular, slopes must be opposite reciprocals.Check slopes for perpendicular: Check if slopes are equal: 4/7 ≠ 3/2, so not parallel.Conclusion: Check if slopes are opposite reciprocals: Reciprocal of 4/7 is 7/4. Opposite of 7/4 is -7/4. But slope of line e is 3/2, not -7/4, so not perpendicular.Since slopes are neither equal nor opposite reciprocals, lines d and e are neither parallel nor perpendicular.

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Math Problems

Algebra 1

Slopes of parallel and perpendicular lines

Full solution

Q. Line

d

has a slope of

\frac{4}{7}

. Line

e

has a slope of

\frac{3}{2}

. Are line

d

and line

e

parallel or perpendicular?

\newline

Choices:

\newline

(A) parallel

\newline

(B) perpendicular

\newline

Check slopes for parallel: Line $d$ slope: $\frac{4}{7}$ . Line $e$ slope: $\frac{3}{2}$ . To be parallel, slopes must be equal. To be perpendicular, slopes must be opposite reciprocals.
Check slopes for perpendicular: Check if slopes are equal: $\frac{4}{7} \neq \frac{3}{2}$ , so not parallel.
Conclusion: Check if slopes are opposite reciprocals: Reciprocal of $\frac{4}{7}$ is $\frac{7}{4}$ . Opposite of $\frac{7}{4}$ is $-\frac{7}{4}$ . But slope of line $e$ is $\frac{3}{2}$ , not $-\frac{7}{4}$ , so not perpendicular.
Conclusion: Check if slopes are opposite reciprocals: Reciprocal of $\frac{4}{7}$ is $\frac{7}{4}$ . Opposite of $\frac{7}{4}$ is $-\frac{7}{4}$ . But slope of line $e$ is $\frac{3}{2}$ , not $-\frac{7}{4}$ , so not perpendicular.Since slopes are neither equal nor opposite reciprocals, lines $d$ and $e$ are neither parallel nor perpendicular.