To solve the problem:

We need to find the equation of a line with the given slope $m = -\frac{1}{4}$ and $y$-intercept $b = \frac{5}{4}$. The general form for a line in slope-intercept form is:

$y = mx + b$

Substituting $m = -\frac{1}{4}$ and $b = \frac{5}{4}$, the equation becomes:

$y = -\frac{1}{4}x + \frac{5}{4}$

To match this with the given answer choices, convert it to standard form, $Ax + By = C$, where $A, B,$ and $C$ are integers. Multiply through by 4 to eliminate the fractions:

$4y = -x + 5$

Rearrange to:

$x + 4y = 5$

This matches option A.

Final Answer: A

Would you like further details or have any questions?
Here are 5 related questions to explore:

1. How can you derive the slope-intercept form from the general form of a line?
2. Why is multiplying through by 4 necessary to simplify the equation?
3. How do we determine the slope and $y$-intercept from standard form equations?
4. What are some alternative methods to verify the solution?
5. Can you rewrite the equation in point-slope form?

Tip: Always ensure the slope and $y$-intercept align with the question's parameters when converting between forms.