Question

If the line is dilated by a factor of 1/3 , what is the equation of the resulting line?

Answer 1

The equation of a line on the plane is of the form
`f(x)=mx+b`, with m and b real numbers.

• If the line is vertically dilated by a factor of
  `(1)/(3)`, then the equation of the resulting line g(x) is
  `g(x)=(1)/(3)f(x)=(mx+b)/(3)=(m)/(3)x+(b)/(3)`.
• If the line is horizontally dilated by a factor of
  `(1)/(3)`, then the equation of the resulting line g(x) is
  `g(x)=f((1)/(3)x)=m((1)/(3)x)+b=(m)/(3)x+b`.