How would I solve this problem?

Question

Find the equation of the line that passes through the point (4, 14) and is perpendicular to

y = 4x + 6

Answer 1

y = 4x + 6 has a slope of 4.
A line that is perpendicular will have a slope of -1/4 (it's the negative reicprocal).
So m = -1/4
y = mx + b can be used.
y = (-1/4)x + b
Substitute in the given point for x and y.
14 = (-1/4)(4) + b
14 = -1 + b
15 = b
Answer: y = (-1/4)x + 15

Answer 2

If it is perpendicluar to the line y = 4x + 6, then its' slope is the negative inverse of the other line. Since the line y = 4x + 6 has a slope of 4 (y = mx + b where m is the slope and b is the y intercept), then the slope of the perpendicular line would be -1/4. So you have the equation:

y = -1/4 x + b.

Plug in your points for x and y and solve for b

14 = -1/4(4) +b
14 = -1 + b
b = 15

the equation of the line perpendicular to y = 4x + 6, passing through (4,14) is y = x/4 + 15

Answer 3

OK, your equation is y = 4x + 6.
That equation's slope = rise over run = 4 upward for each 1 you move right.

A perpendicular line would have to go 4 right for each 1 you move down. This translates to a slope of -1/4.

Hence, the problem turns into: Find a line with equation y = (-1/4)x + b, which passes through (4,14).

To figure out b, plug in the points into the equation.

14 = (-1/4)*4 + b
14 = -1 + b
so b = 15

The equation is y = (-1/4)x + 15.

Answer 4

LIne y = 4x + 6 has a slope of 4.
A line that is perpendicular will have a slope of -1/m where m is the slope of actual line.Here m = 4
so writing equation in form of
y = (-1/4)x + c
and usng the point (4,14) lying over it
14 = (-1/4)(4) + c
14 = -1 + c
15 = c
hence equation of perpendicular line is given as
y = (-1/4)x + 15

Answer 5

Since its perpendicular to y=4x+6, the slope of the required line would be the negative inverse of this line i.e.
m=-(1/4)

Using the formula,(y-y1)=m(x-x1)
y-14=-(1/4)(x-4)
4y-56+x=4
x+4y=60

Answer 6

m=-1/4 then
y=-1/4(x-4)+14
y=-1/4x+1+14
y=-1/4x+15 <== answer