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To find the equation of a line in slope-intercept form, \( y = mx + b \), we need the slope \( m \) and the y-intercept \( b \).

### Given:
- Point: \( (4, 1) \)
- Slope: \( m = -\frac{5}{4} \)

### Steps:
1. **Use the point-slope form** of the equation of a line:  
   \[
   y - y_1 = m(x - x_1)
   \]
   where \( (x_1, y_1) \) is a point on the line.
   
2. **Substitute** the given point \( (4, 1) \) and the slope \( -\frac{5}{4} \):
   \[
   y - 1 = -\frac{5}{4}(x - 4)
   \]

3. **Expand** the equation:
   \[
   y - 1 = -\frac{5}{4}x + \frac{5}{4} \cdot 4
   \]
   \[
   y - 1 = -\frac{5}{4}x + 5
   \]

4. **Solve for \( y \)** to put the equation in slope-intercept form:
   \[
   y = -\frac{5}{4}x + 5 + 1
   \]
   \[
   y = -\frac{5}{4}x + 6
   \]

### Final Answer:
The equation of the line in slope-intercept form is:
\[
y = -\frac{5}{4}x + 6
\]

Would you like more details on any part of this process? 

Here are five related questions for further exploration:
1. How do you find the equation of a line given two points instead of a point and a slope?
2. What does the slope of a line represent geometrically?
3. How can you determine if two lines are parallel or perpendicular?
4. How do you convert a line equation from slope-intercept form to standard form?
5. How do you find the x-intercept of a line given its slope-intercept equation?

**Tip:** In slope-intercept form, the coefficient of \( x \) represents the slope, and the constant term represents the y-intercept directly.

A line passes through the point (4, 1) and has a slope of -5/4. Write an equation in slope-intercept form for this line.

Learn how to write the equation of a line that passes through the point (4, 1) with a slope of -5/4. This algebra problem focuses on using the point-slope form and converting to slope-intercept form. Suitable for Grades 8-10 students.

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