Question

Which of these is a point-slope equation of the line that is perpendicular to y-3=4(x-10) and passes through (-3,7)?

A. y+7= -1/4(x-3)
B. y-7= -1/4(x+3)
C.y+7= 4(x-3)
D.y-7= -4(x+3)

Answer 1

B

Explanation:

The point slope form of a line is
`(y-y_1)=m(x-x_1)` where
`x_1=-3\\y_1=7`. We can find the slope which is perpendicular to the slope of 4 in the equation y=4(x-10). Perpendicular slope is the negative reciprocal which is -1/4.

We write

`(y-7)=-(1)/(4)(x--3)\\(y-7)=-(1)/(4)(x+3)`