In order to solve this problem we have to remember that the equation of any line takes the form
[tex]y(x)=mx+b[/tex]
Therefore,
[tex]y(kx)=\text{mkx}+b[/tex]
In other words, multiplying k by x is just multiplying the slope m by a factor of k.
The slope of g(x) is
[tex]m=2[/tex]
and the slope of f(x) is
[tex]m=1[/tex]
We see than the slope of g(x) is 2 times the slope of f(x); therefore, k = 2 which is choice D.
