determine b so that the line with equation 5x + by - 6 = 0 is perprdicular to the line with equation 7y = 4x + 7
1 answer:
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Answer:
b = 20/7
Step-by-step explanation:
The slope of the first line can be found by solving for y:
by = -5x +6 . . . . . . add 6-5x
y = -5/b +6/b . . . . . divide by b
The slope is -5/b.
The slope of the second line can be found by solving for y:
7y = 4x +7
y = 4/7x +1 . . . . . . divide by 7
The slope is 4/7.
For the lines to be perpendicular, the product of these slopes must be -1:
(-5/b)(4/7) = -1
-20/(7b) = -1 . . . . simplify
b = 20/7 . . . . . . . multiply by -b
The lines will be perpendicular when b = 20/7.
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