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Determine from the given points of two lines if the lines are parallel, perpendicular, or neither. Line a: (-3, 1) and (-7, -2)Line b: (2, -1) and (8, 4)What is the slope of line a?What is the slope of line b?Are the slopes the same?Are the slopes opposite recipricals?Are the lines perpendicular, parallel, or neither?

User Francesco Puglisi
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1 Answer

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ANSWER

• Slope of line a: 3/4

,

• Slope of line b: 5/6

,

• The lines are ,neither parallel nor perpendicular

Step-by-step explanation

The slope of a line that passes through points (x₁, y₁) and (x₂, y₂) is,


m=(y_1-y_2)/(x_1-x_2)

Line a passes through the points (-3, 1) and (-7, -2). Its slope is,


m_a=(1-(-2))/(-3-(-7))=(1+2)/(-3+7)=(3)/(4)

Line b passes through the points (2, -1) and (8, 4). Its slope is,


m_b=(-1-4)/(2-8)=(-5)/(-6)=(5)/(6)

Two lines are parallel if they have the same slope, and they are perpendicular if they have opposite reciprocal slopes.

In this case, the slopes of lines a and b are different, so they are not parallel. They are not opposite reciprocal either, so they are not perpendicular. Hence, the lines are neither parallel nor perpendicular.

User Barremian
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