We are given:

• A point $(-4, -8)$.
• A slope of $\frac{5}{4}$.

We need to find the equation of the line in slope-intercept form, which is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

Step-by-Step Solution:

1. Use the point-slope form of the line equation: The point-slope form is given by: $y - y_1 = m(x - x_1)$ where $(x_1, y_1)$ is the point on the line and $m$ is the slope.

2. Plug in the given values:

   • Slope $m = \frac{5}{4}$,
   • Point $(x_1, y_1) = (-4, -8)$.

   So, the point-slope equation becomes: $y - (-8) = \frac{5}{4}(x - (-4))$ which simplifies to: $y + 8 = \frac{5}{4}(x + 4)$

3. Expand and solve for $y$: $y + 8 = \frac{5}{4}x + \frac{5}{4} \cdot 4$ $y + 8 = \frac{5}{4}x + 5$

4. Isolate $y$: $y = \frac{5}{4}x + 5 - 8$ $y = \frac{5}{4}x - 3$

Final Answer:

The equation of the line in slope-intercept form is: $y = \frac{5}{4}x - 3$

Would you like further details on how each step was completed or have any questions? Here are five related questions to explore:

1. How do you find the equation of a line if given two points instead of a point and a slope?
2. What is the significance of the slope and y-intercept in the equation of a line?
3. Can you convert a line equation from standard form to slope-intercept form?
4. What does a slope of $\frac{5}{4}$ indicate about the steepness of the line?
5. How would the equation change if the slope was negative instead?

Tip: When dealing with equations of lines, always double-check your arithmetic and signs to avoid common mistakes.