Question

What is an equation of the line that is perpendicular to y-4=2(x-6) and passes through the point (-3,-5)

Answer 1

`y+5=-(1)/(2)(x+3)`

Explanation:

The given equation is

`y-4=2(x-6)`

This equation is in the point-slope form,
`y-y_1=m(x-x_1)`, where
`m=2` is the slope of this line.

The line that is perpendicular to this line has slope
`-(1)/(2)`

If this line that is perpendicular to the given line passes through (-3,-5), then it will have equation;

`y--5=-(1)/(2)(x--3)`

`y+5=-(1)/(2)(x+3)` in point-slope form

Answer 2

y+5 = -1/2(x + 3)

Explanation:

Perpendicular lines have negative reciprocal slopes. The slope of the line

y - 4 = 2(x - 6) is 2. Its negative reciprocal slope is -1/2.

Using m = -1/2 and the point (-3,-5) in the point slope form.

y --5 = -1/2(x--3)

y+5 = -1/2(x + 3)