Question

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Answer 1

Answer: Choice C
`y + 7 = -(4)/(5)(x-6)`

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Step-by-step explanation:

The given equation
`y = (5)/(4)x-5` is in the form
`y = mx+b` with slope
`m = (5)/(4)`

Apply the negative reciprocal to
`(5)/(4)` to get
`-(4)/(5)`. We flipped the fraction and the sign from positive to negative. The perpendicular slope is
`-(4)/(5)`

With any two perpendicular lines, their slopes always multiply to -1. This is assuming neither line is a vertical line. In this case:
`(5)/(4) * (-4)/(5) = -1`

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We'll now let
`m = -(4)/(5)` and
`(x_1,y_1) = (6,-7)`

Plug these three pieces of information into the point-slope formula

`y - y_1 = m(x - x_1)\\\\y - (-7) = -(4)/(5)(x - 6)\\\\y + 7 = -(4)/(5)(x - 6)`

This points to choice C as the final answer.