F(x)=4x+5 passing through the point (16,2) write an equation for a line perpendicular

Answer 1

The slope is 4 so the perpendicular slope is the negative reciprocal which is -1/4.

We will plug the point (16,4)into the equation y = -(1/4)x + b to find b.

2 = - (1/4)16 + b

2 = -4 + b

b = 6

y = -(1/4)x + 6 is the answer

Or you could say F(x) = -(1/4)x + 6

Answer 2

You want a line perpendicular to F(x) = 4x + 5 that passes through the point (16,2). The wording of this problem isn't the best.

First, perpendicular lines have slopes that are opposite and reciprocals of each other. The first line has a slope of 4, so our new line much have a slope of -1/4

We also know a point that our new line goes through: (16,2)

You know the slope of the line and a point the line goes through so use the point-slope equation for a line

y - y₁ = m(x - x₁)