https://file.aiquickdraw.com/mathbot/file/1728843403852krd572es.jpg

To solve this problem, we need to graph the line based on the given information and match it to one of the options provided. 

### Given Equation
The line has the following characteristics:
- Slope, \( m = -\frac{1}{4} \)
- Y-intercept, \( b = 6 \)

The equation of a line in slope-intercept form is:
\[
y = mx + b
\]

Substitute the given slope and y-intercept into the equation:
\[
y = -\frac{1}{4}x + 6
\]

### Graphing the Line
1. **Y-Intercept**: The y-intercept is at \( b = 6 \). This means the line will cross the y-axis at the point \( (0, 6) \).
2. **Slope**: The slope \( m = -\frac{1}{4} \) indicates that for every 4 units we move to the right, the line moves down 1 unit. This results in a downward-sloping line.

#### Steps to Plot:
1. Start at the y-intercept point \( (0, 6) \).
2. From this point, apply the slope:
   - Move 4 units to the right (positive x-direction).
   - Move 1 unit down (negative y-direction).
3. This should give the next point at \( (4, 5) \).
4. Draw a line through these points, maintaining the same slope.

### Matching with the Options
After reviewing the choices:
- **Option C** best matches the description**. It has a y-intercept at \( 6 \) and a negative slope that appears consistent with \( -\frac{1}{4} \).

Thus, the correct answer is **C**.

Would you like a further explanation of the steps, or do you have any questions?

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#### Follow-Up Questions:
1. How do you determine the y-intercept of a line from an equation?
2. What is the impact of a negative slope on the direction of a line?
3. How would you graph a line if the slope is positive instead of negative?
4. Can you convert the slope-intercept form to standard form?
5. How can you check if a point lies on a specific line?

#### Tip:
Remember that the y-intercept is where the line crosses the y-axis, and the slope tells you how steep the line is and the direction it moves as you go from left to right.

Graph the line for the equation with slope m = -1/4 and y-intercept b = 6. Choose the correct graph from the given options.

Learn how to graph the line y = -1/4x + 6, identifying the correct graph from multiple options. This problem focuses on using the slope-intercept form of linear equations and interpreting slope and y-intercept. Suitable for students in Grades 8-10.

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