Determine whether the lines for each pair of equations 3x+2y=-5 y=-2/3x+6 are parallel, perpendicular, or neither

Inbrunstlr 2022-10-08 Answered
Determine whether the lines for each pair of equations 3x+2y=-5 y=-2/3x+6 are parallel, perpendicular, or neither
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Answers (2)

Mckenna Friedman
Answered 2022-10-09 Author has 10 answers
First, we get the two linear equations into y=mx+b form:
L 1 : y = - 2 3 x + 6 m = - 2 3
L 2 : 3 x + 2 y = - 5
L 2 : 2 y = - 3 x - 5
L 2 : y = - 3 2 x - 5 m = - 3 2
If the lines were parallell, they would have the same m-value, which they don't, so they cannot be parallell.
If the two lines are perpendicular, their m-values would be negative reciprocals of each other. In the case of L 1 , the negative reciprocal would be:
- 1 - 2 3 = - ( - 3 2 ) = 3 2
This is almost the negative reciprocal, but we're off by a minus sign, so the lines are not perpendicular.
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Denisse Fitzpatrick
Answered 2022-10-10 Author has 3 answers
Rearranging the 1 st equation as y=mx+c,we get,
y = - 3 2 x - ( 5 2 ) hence, slope = - 3 2
the other equation is, y = - 2 3 x + 6 ,slope is - 2 3
Now,slope of both the equations are not equal,so they are not parallel lines.
Again,product of their slope is - 3 2 ( - 2 3 ) = 1
But,for two lines to be perpendicular, product of their slope has to be −1
So,they are not perpendicular as well.
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