Question

What is the equation of the line perpendicular to `y=-3/7x+12` at `x=-1`?

Answer 1

`y = (7/3)x + (310/21)`

Explanation:

Perpendicular means that the slopes will be opposite, so the slope is (7/3). At x = -1 the original line y value is `12+3/7` or `(87/7)`.
To find the new constant at that point we put it into the new equation.
`y = (7/3)x + b` ; `(87/7) = (7/3)(-1) + b` ; `(87/7) + (7/3) = b` ; `(261/21) + (49/21) = b`

`(310/21) = b`
So the new line equation is `y = (7/3)x + (310/21)`

CHECK: At (-1, (87/7)) `(87/7) = (7/3)(-1) + (310/21)`

`(87/7) = -(49/21) + (310/21)` ; `(87/7) = (261/21)`
`(87/7) = (87/7)` Correct!