Answer
$L(x)=\frac{\sqrt{20x^2-20x+25}}{4}$
Work Step by Step
$\mathrm{See\:the\:figure\:below.}$ When you have any point in a plane, you can use the Pythagorean theorem to determine the distance to the origin.
$L=\sqrt{x^2+y^2}$
From the given function $\ 2y+4y=5,\ $ we can express $\ y\ $ as a function of $\ x.$
$2x+4y=5$
$\Rightarrow\ 4y=5-2x$
$\Rightarrow\ y=\frac{5-2x}{4}$
Plug in the expression for $\ y\ $ to get $\ L\ $ as a function of $\ x.$
$L=\sqrt{x^2+(\frac{5-2x}{4})^2}$
$\Rightarrow\ L=\frac{\sqrt{20x^2-20x+25}}{4}$
