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7-110.

Find the slope of each line below. Which pairs of lines are perpendicular? Which pairs are parallel?

Slopes that are opposite reciprocals of each other are perpendicular, while parallel lines share the same slope.

1. $y=\frac{-5}{6}x+3$

Slope is given in the equation.

1. $y=3$

$y = 3$ is a horizontal line, thus its slope is zero.

1. $5x+6y=9$

Rearrange the equation into the $y = mx + b$ form to identify the slope.

1. $x=−4$

$x = −4$ is a vertical line, thus its slope is undefined.

1. $y=−4x−5$

Slope is given.

1. $y=\frac{1}{4}x-7$

Slope is given.

1. $4x−y=2$

Rearrange the equation into the $y = mx + b$ form to identify the slope.

1. $y=5-\frac{6}{5}x$

Rearrange slightly and identify the slope.

An example of a pair of parallel lines is the line from part (a) and the line from part (c), while an example of a pair of perpendicular
lines is the line from part (b) and the line from part (d). Knowing this information, can you find your own examples?