Two of the forms of the equation of the line are:
[tex]\begin{gathered} y=mx+b\Rightarrow\text{ Slope-intercept form} \\ ax+by=c\Rightarrow\text{ Standard form } \end{gathered}[/tex]To take the equation of the line from its slope-intercept form to its standard form, just solve for the constant:
[tex]\begin{gathered} y=-\frac{5}{4}x-4 \\ \text{ Multiply by 4 from both sides of the equation} \\ 4y=4\cdot(-\frac{5}{4}x-4) \\ 4y=-5x-16 \\ \text{ Add 5x from both sides of the equation} \\ 4y+5x=-5x-16+5x \\ 4y+5x=-16 \\ \text{ Reorder} \\ 5x+4y=-16 \end{gathered}[/tex]Therefore, the equation of the line in its standard form is
[tex]5x+4y=-16[/tex]