We need to find the equation of a line given the slope $m = -4$ and the point $(5,8)$.

Step 1: Use the point-slope form of a line

The point-slope form is:
$y - y_1 = m(x - x_1)$ Substituting $m = -4$, $x_1 = 5$, and $y_1 = 8$:
$y - 8 = -4(x - 5)$

Step 2: Expand and simplify

$y - 8 = -4x + 20$ $y = -4x + 28$

Final Answer

$y = -4x + 28$

Let me know if you want a more detailed explanation!

Here are five related questions to expand your understanding:

1. How do you convert a line equation from point-slope form to standard form?
2. What does the slope represent in a real-world context?
3. How do you determine if two lines are parallel or perpendicular?
4. Can you find the x-intercept of this line?
5. How would the equation change if the given point was different?

Tip: When using the point-slope formula, always distribute carefully to avoid sign mistakes.