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To find the equation of the line in **slope-intercept form** \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept, follow these steps:

### Given Information:
- **Point**: \( (6, -7) \)
- **Slope** \( (m) = -\frac{4}{3} \)

### Solution:
1. **Start with the slope-intercept form**:
   \[
   y = mx + b
   \]

2. **Substitute the slope** \( m = -\frac{4}{3} \):
   \[
   y = -\frac{4}{3}x + b
   \]

3. **Use the point \( (6, -7) \) to find \( b \)**:
   Substitute \( x = 6 \) and \( y = -7 \) into the equation.
   \[
   -7 = -\frac{4}{3}(6) + b
   \]

4. **Simplify**:
   \[
   -7 = -8 + b
   \]

5. **Solve for \( b \)**:
   \[
   b = -7 + 8 = 1
   \]

6. **Write the final equation**:
   \[
   y = -\frac{4}{3}x + 1
   \]

### Answer:
The equation of the line in slope-intercept form is:
\[
y = -\frac{4}{3}x + 1
\]

Would you like further details on any part of the solution?

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Here are 5 related questions for further practice:
1. How would the equation change if the slope were positive \( \frac{4}{3} \) instead?
2. What is the equation of a line parallel to this one that passes through the origin?
3. How do you determine if two lines are perpendicular?
4. Can you find the x-intercept of the line \( y = -\frac{4}{3}x + 1 \)?
5. How would you write the equation if given two points instead of a point and a slope?

**Tip:** When finding the y-intercept \( b \), substitute the coordinates of the known point and the slope into the equation, then solve for \( b \).

A line passes through the point (6, -7) and has a slope of -4/3. Write an equation in slope-intercept form for this line.

Learn how to write the equation of a line passing through a point (6, -7) with a slope of -4/3 in slope-intercept form. This example covers key algebra concepts and step-by-step solutions for finding the equation of a line.

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