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Line $p$ has a slope of $\frac{7}{6}$ . Line $q$ has a slope of $\frac{7}{6}$ . Are line $p$ and line $q$ 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

p

has a slope of

\frac{7}{6}

. Line

q

has a slope of

\frac{7}{6}

. Are line

p

and line

q

parallel or perpendicular?

\newline

Choices:

\newline

(A) parallel

\newline

(B) perpendicular

\newline

(C) neither

Slope Equality Implies Parallel Lines: Line $p$ has a slope of $\frac{7}{6}$ , and line $q$ also has a slope of $\frac{7}{6}$ , so what does that tell us about the lines? $\newline$ Since both lines have the same slope, they are parallel to each other.
Parallel Lines and Equal Slopes: Parallel lines have equal slopes, so if line $p$ and line $q$ have the same slope, they are parallel.
Not Perpendicular Due to Equal Slopes: Since the slopes are equal and not the negative reciprocal of each other, the lines are not perpendicular.
Conclusion: Lines are Parallel: So, the answer to whether line $p$ and line $q$ are parallel or perpendicular is that they are parallel.

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