The given equation is:

$4x - 20y = -160$

We need to convert this into slope-intercept form, $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

Steps:

1. Isolate $y$:

   Subtract $4x$ from both sides: $-20y = -4x - 160$

2. Divide through by $-20$: $y = \frac{-4x - 160}{-20}$

   Simplify each term: $y = \frac{-4}{-20}x + \frac{-160}{-20}$

   $y = \frac{1}{5}x + 8$

Final Answer:

$y = \frac{1}{5}x + 8$

Would you like further clarification or details?

Follow-up questions:

1. What does the slope $\frac{1}{5}$ represent in this context?
2. How would you graph this equation using its slope and y-intercept?
3. Can this equation be rewritten in standard form again from slope-intercept form?
4. How does the y-intercept change the position of the line on a graph?
5. What is the x-intercept of this equation?

Tip: Always double-check your slope-intercept form by substituting values for $x$ to ensure the equation holds true!