The equation provided is $y = -4x - 1$, which is in slope-intercept form: $y = mx + b$.

• Slope (m): The slope is $-4$, meaning for every 1 unit increase in $x$, $y$ decreases by 4 units.
• Y-intercept (b): The y-intercept is $-1$, meaning the graph crosses the y-axis at $(0, -1)$.

Steps to graph:

1. Plot the y-intercept: Start by marking the point $(0, -1)$ on the graph.
2. Use the slope: From the y-intercept, move according to the slope. Since the slope is $-4$, go down 4 units and right 1 unit to find another point. This would give the point $(1, -5)$.
3. Continue plotting: You can continue plotting more points by moving again by the slope's rule: down 4 units and right 1 unit for each new point.
4. Draw the line: Once you have a couple of points, draw a straight line through them to complete the graph.

Let me know if you would like a graph or more explanation!

Would you like a more detailed explanation or graph assistance? Here are some additional questions to expand on:

1. What does the slope of a line represent in different contexts?
2. How would changing the slope from $-4$ to a different number affect the graph?
3. How does the y-intercept influence where the line is positioned?
4. Can you derive an equation from a graph if only the points are given?
5. What happens if we change the equation to $y = -4x + 1$?

Tip: When graphing linear equations, always start with the y-intercept and use the slope to find more points!