To graph the line given by the equation $y = -6x + 5$, we'll use the slope-intercept form $y = mx + b$, where:

• $m$ is the slope
• $b$ is the y-intercept

In this equation:

• The slope $m = -6$ means the line goes down 6 units for every 1 unit it moves to the right.
• The y-intercept $b = 5$ means the line crosses the y-axis at $(0, 5)$.

Steps to graph the line:

1. Plot the y-intercept: Start by plotting the point $(0, 5)$ on the graph (the y-axis at 5).
2. Use the slope: From the point $(0, 5)$, use the slope $m = -6$. This means you move down 6 units and right 1 unit to find another point on the line.
   • Start from $(0, 5)$ and move to $(1, -1)$.
3. Draw the line: Connect the two points with a straight line.

Let me know if you'd like a visual representation, or if you need further assistance!

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Additional questions to explore:

1. How do you graph a line given the slope and y-intercept?
2. What does the slope represent in real-world terms?
3. How can you find the equation of a line if you're given two points on it?
4. What happens to the graph of the line if the slope is positive instead of negative?
5. How would you graph a line if the equation was in point-slope form?

Tip: When plotting lines, always start with the y-intercept, and then use the slope to guide your points accurately!