#### Answer

$\text{Slope-Intercept Form: }
y=4x
\\\text{Standard Form: }
4x-y=0$

#### Work Step by Step

Use the Two-Point Form of linear equations to find the equation of the line passing through $(
0,0
)$ and $(
1,4
).$
Using $y-y_1=\dfrac{y_1-y_2}{x_1-x_2}(x-x_1)$ or the Two-Point Form of linear equations, the equation of the line with the given conditions is
\begin{array}{l}\require{cancel}
y-0=\dfrac{0-4}{0-1}(x-0)
\\\\
y=\dfrac{-4}{-1}x
\\\\
y=4x
.\end{array}
Using $y=mx+b$ or the Slope-Intercept Form of linear equations, the equation above is equivalent to
\begin{array}{l}\require{cancel}
y=4x+0
\\\\
y=4x
.\end{array}
Using $Ax+By=C$ or the Standard Form of linear equations, the equation above is equivalent to
\begin{array}{l}\require{cancel}
-4x+y=0
\\\\
4x-y=0
.\end{array}
Hence, the equation of the line is
\begin{array}{l}\require{cancel}
\text{Slope-Intercept Form: }
y=4x
\\\text{Standard Form: }
4x-y=0
.\end{array}