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

Line Slopes Comparison: Line a slope: 9/5. Line b slope: 5/9. If they're parallel, slopes should be equal. If they're perpendicular, slopes should be opposite reciprocals.Check Slope Equality: Check if slopes are equal: 9/5 = 5/9? Nope, they're not equal.Check Opposite Reciprocal: Check if slopes are opposite reciprocals: Is 9/5 the opposite reciprocal of 5/9? Multiply 9/5 by 5/9, if it equals -1, they're perpendicular.Perpendicularity Calculation: Calculation: (9/5) * (5/9) = 45/45 = 1. But we need -1 for them to be perpendicular. So, they're neither parallel nor perpendicular.

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Math Problems

Algebra 1

Slopes of parallel and perpendicular lines

Full solution

Q. Line

a

has a slope of

\frac{9}{5}

. Line

b

has a slope of

\frac{5}{9}

. Are line

a

and line

b

parallel or perpendicular?

\newline

Choices:

\newline

(A) parallel

\newline

(B) perpendicular

\newline

Line Slopes Comparison: Line $a$ slope: $\frac{9}{5}$ . Line $b$ slope: $\frac{5}{9}$ . If they're parallel, slopes should be equal. If they're perpendicular, slopes should be opposite reciprocals.
Check Slope Equality: Check if slopes are equal: $\frac{9}{5} = \frac{5}{9}$ ? Nope, they're not equal.
Check Opposite Reciprocal: Check if slopes are opposite reciprocals: Is $\frac{9}{5}$ the opposite reciprocal of $\frac{5}{9}$ ? Multiply $\frac{9}{5}$ by $\frac{5}{9}$ , if it equals $-1$ , they're perpendicular.
Perpendicularity Calculation: Calculation: $(\frac{9}{5}) \times (\frac{5}{9}) = \frac{45}{45} = 1$ . But we need $-1$ for them to be perpendicular. So, they're neither parallel nor perpendicular.