The equation you provided is \( Y = \frac{1}{4}x + 9 \).

This is the equation of a straight line in slope-intercept form \( Y = mx + b \), where:

- \( m \) is the slope, and in this case, \( m = \frac{1}{4} \).
- \( b \) is the y-intercept, and in this case, \( b = 9 \).

### Key Points:
1. **Slope**: The slope \( \frac{1}{4} \) indicates that for every increase of 4 units in the x-direction, the value of \( Y \) increases by 1 unit.
2. **Y-intercept**: The line crosses the Y-axis at \( Y = 9 \).
3. **X-intercept**: You can find where the line crosses the X-axis by setting \( Y = 0 \) and solving for \( x \):
   \[
   0 = \frac{1}{4}x + 9
   \]
   Solving this, we get:
   \[
   x = -36
   \]

Would you like more details or have any questions on this?

Here are some related questions:
1. How do you find the slope of a line from two points?
2. How can you convert this equation to standard form?
3. How does changing the slope affect the steepness of the line?
4. What is the significance of the y-intercept in real-life problems?
5. How would the equation change if the slope were negative?

**Tip**: To graph a line, it's often easiest to plot the y-intercept first and then use the slope to find other points.

Explore how to solve the linear equation Y = (1/4)x + 9. Learn about the slope, y-intercept, and x-intercept of the line. This step-by-step guide covers essential algebraic concepts and formulas, suitable for students in Grades 8-10.

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