Question

Find the equation of the line that passes through the point (-8,15) and is perpendicular to the equation below.

y = -4/5x + 5

A. y = -5/4x + 5
B. y = -4/5x - 7
C. y = -4/5x + 23
D. y = 5/4x + 25
Please help asap!

Answer 1

`y = (5)/(4) x + 25`

Explanation:

We were told that the equation of the line we are looking for is perpendicular to

`y = - (4)/(5) x + 5`

We know that the gradient of perpendicular lines when multiplied is equal to -1, therefore

`line \: .1 * \: line \: .2 = - 1 \\ \\ (4)/(5) * line \: .2 = - 1 \\ \\ line \: .2 = ( - 1)/( (4)/(5) )`

`line\: .2 = (5)/(4) \: \: \: \: y = 15 \: \: \: \: x = - 8 \\ \\ y = mx + c \\ \\15 = ( (5)/(4) ) - 8 + c \\ \\ 15 = - 10 + c \\ 15 + 10 = c`

`25 = c \\ \\ therefore \: the \: equation \: of \: the \: line \: is \: \\ \\ y = (5)/(4) x + 25`