Let P(x,y) be a point on the graph of f(x)=3x-2 graph. Express the distance d from p to (3,4) as a function of x.

Question

Please describe each step carefully!

Answer 1

Hi Crystal:

 

Since the point P(x,y) is on the graph of y = 3x-2 then the

point P can be expressed as (x, 3x-2).  We want the distance

from (3,4) to (x, 3x-2)

 

Using the distance formula the distance from (x₁,y₁) to (x₂,y₂) is:

d = √[(x₂ - x₁)² + (y₂-y₁)²]

 

d = √[(x-3)² + (3x-2-4)²]

 

d =  √[(x²-6x+9)+(3x-6)²]

 

d = √(x²-6x+9+9x²-36x+36)

 

d =  √(10x²-42x+45)

 

Does this make sense to you?