SOLUTION: Determine whether each pair of lines are parallel, perpendicular, or neither.
a. 6x=5y+1 and -12x+10y=1
b. 6+4x=3y and 3x+4y=8
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Question 1047230: Determine whether each pair of lines are parallel, perpendicular, or neither.
a. 6x=5y+1 and -12x+10y=1
b. 6+4x=3y and 3x+4y=8
Found 2 solutions by Alan3354, rothauserc:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Find the slope of each line.
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If the slopes are equal, they're parallel.
If the product of the 2 slopes = -1, ie, if m1 = -1/m2, they're perpendicular.
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If neither, they're neither.
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
To solve the problems, we need to arrange the equations into the slope-intercept form
:
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a) 6x=5y+1 and -12x+10y=1
:
5y = -6x +1
y = (-6x/5) +(1/5)
:
10y = 12x +1
y = (12x/10) +(1/10)
y = (6x/5) +(1/10)
:
If the slopes are equal, then the lines are parallel
If the slopes are negative reciprocals, then the lines are perpendicular
:
The slopes are -6/5 and 5/5, the lines are neither parallel or perpendicular
:
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:
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b) 6+4x=3y and 3x+4y=8
:
3y = 4x +6
y = (4x/3) +2
:
4y = -3x +8
y = (-3x/4) +2
:
The slopes are 4/3 and -3/4, the lines are perpendicular
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:
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