Question

determine b so that the line with equation 5x + by - 6 = 0 is perprdicular to the line with equation 7y = 4x + 7

Answer 1

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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.