ANSWER
The equation is
[tex]y = 4x[/tex]
EXPLANATION
The given function goes through the origin so its equation is of the form
[tex]y = mx[/tex]
where m is the slope of the graph of the function.
Since the straight line goes through
[tex](0,0) \: and \: (2,8)[/tex]
we can use these points to determine the slope using the slope formula
[tex]m = \frac{y_2-y_1}{x_2-x_1} [/tex]
This implies that,
[tex]m = \frac{8 - 0}{2 - 0} [/tex]
[tex]m = \frac{8}{2} = 4[/tex]
We substitute the slope into the formula to get,
[tex]y = 4x[/tex]
as the required equation.
Therefore the correct answer is D.
