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

Line Slopes Comparison: Line a slope: 7/4. Line b slope: 4/7. Are they the same or opposite reciprocals?Parallel and Perpendicular Lines: If lines are parallel, their slopes are equal. If perpendicular, their slopes are opposite reciprocals. Check if 7/4 is the opposite reciprocal of 4/7.Opposite Reciprocal Calculation: Opposite reciprocal of 7/4 is -4/7. But line b's slope is positive 4/7.Conclusion: Since 7/4 is not equal to 4/7, lines a and b are not parallel. Since 7/4 is not the opposite reciprocal of 4/7, lines a and b are not perpendicular.

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Line $a$ has a slope of $\frac{7}{4}$ . Line $b$ has a slope of $\frac{4}{7}$ . Are line $a$ and line $b$ parallel or perpendicular? $\newline$ Choices: $\newline$ (A) parallel $\newline$ (B) perpendicular $\newline$ (C) neither

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Math Problems

Algebra 1

Slopes of parallel and perpendicular lines

Full solution

Q. Line

a

has a slope of

\frac{7}{4}

. Line

b

has a slope of

\frac{4}{7}

. Are line

a

and line

b

parallel or perpendicular?

\newline

Choices:

\newline

(A) parallel

\newline

(B) perpendicular

\newline

Line Slopes Comparison: Line $a$ slope: $\frac{7}{4}$ . Line $b$ slope: $\frac{4}{7}$ . Are they the same or opposite reciprocals?
Parallel and Perpendicular Lines: If lines are parallel, their slopes are equal. If perpendicular, their slopes are opposite reciprocals. Check if $\frac{7}{4}$ is the opposite reciprocal of $\frac{4}{7}$ .
Opposite Reciprocal Calculation: Opposite reciprocal of $\frac{7}{4}$ is $-\frac{4}{7}$ . But line $b$ 's slope is positive $\frac{4}{7}$ .
Conclusion: Since $\frac{7}{4}$ is not equal to $\frac{4}{7}$ , lines $a$ and $b$ are not parallel. Since $\frac{7}{4}$ is not the opposite reciprocal of $\frac{4}{7}$ , lines $a$ and $b$ are not perpendicular.