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The task is to graph the equation of a line that has a y-intercept of 6 and a slope of -4.

To derive the equation of the line, we can use the slope-intercept form:

\[
y = mx + b
\]

Where:
- \( m \) is the slope (in this case, \( m = -4 \))
- \( b \) is the y-intercept (in this case, \( b = 6 \))

So, the equation becomes:

\[
y = -4x + 6
\]

### Steps to graph the line:
1. **Plot the y-intercept**: This is the point \( (0, 6) \). On the graph, locate \( y = 6 \) on the y-axis.
2. **Use the slope**: Since the slope is -4, it means for every 1 unit you move to the right along the x-axis, you move 4 units down on the y-axis. From the point \( (0, 6) \), move 1 unit to the right and 4 units down to find another point, which would be \( (1, 2) \).
3. **Draw the line**: Connect these two points, \( (0, 6) \) and \( (1, 2) \), and extend the line in both directions.

This gives you the graph of the line.

Would you like further details on how to calculate slope or verify points?

### Related Questions:
1. What happens if the slope of the line is positive instead of negative?
2. How can you find the x-intercept of this line?
3. What is the meaning of the slope in the context of rate of change?
4. How do parallel lines relate to their slopes?
5. Can you determine the equation of a line given only two points?

**Tip**: The slope tells you how steep a line is. A negative slope means the line descends as you move to the right.

Trazar el gráfico de la recta cuya intersección con el eje y es 6 y pendiente es -4.

Learn how to graph a line with a slope of -4 and a y-intercept of 6 using the slope-intercept form. This algebra problem guides students through plotting the y-intercept and using the slope to draw the line. Ideal for Grades 8-10.

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