Question

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

Answer 1

Answer:

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 $\frac{1}{3}$, then the equation of the resulting line g(x) is $g(x)=\frac{1}{3}f(x)=\frac{mx+b}{3}=\frac{m}{3}x+\frac{b}{3}$.
• If the line is horizontally dilated by a factor of $\frac{1}{3}$, then the equation of the resulting line g(x) is $g(x)=f(\frac{1}{3}x)=m(\frac{1}{3}x)+b=\frac{m}{3}x+b$.