4
QuizMultiple Choice

Equations of Parallel and Perpendicular Lines — Quiz

Question 4 • Algebra: Concepts and Connections

Which statement is true about the graphs of the two lines y is equal to negative 4 fifths x plus 2 and y is equal to negative 5 fourths x minus 1 half ?

Answer
A
The lines are neither parallel nor perpendicular to each other because 2 and negative 1 half are not opposite reciprocals of each other.
B
The lines are neither parallel nor perpendicular to each other because negative 4 fifths and negative 5 fourths are not opposite reciprocals of each other.
C
The lines are perpendicular to each other because 2 and negative 1 half are opposite reciprocals of each other.
D
The lines are perpendicular to each other because negative 4 fifths and negative 5 fourths are opposite reciprocals of each other.

Explanation

In slope-intercept form, the slopes are −4/5 and −5/4. Perpendicular lines have slopes that are negative reciprocals, so their product must be −1; here the product is (−4/5)(−5/4) = 1. The slopes are also unequal, so the lines are not parallel. Thus, they are neither parallel nor perpendicular, as stated in choice A.

AI-written and checked against the verified answer.

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