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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.

A line passes through the point (-4, -8) and has a slope of 5/4. Write an equation in slope-intercept form for this line.

Learn how to find the equation of a line that passes through the point (-4, -8) with a slope of 5/4. Step-by-step explanation using the slope-intercept form y = mx + b. Suitable for students in Grades 8-10.

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