The equation to graph is $y = -6x + 8$. Here's how you can graph this line using its slope and $y$-intercept:

1. Identify the y-intercept:
   The $y$-intercept is where $x = 0$. From the equation, the $y$-intercept is $8$. So the point $(0, 8)$ is one point on the line.

2. Use the slope to find another point:
   The slope of the line is $-6$, which means for every 1 unit increase in $x$, $y$ decreases by 6 units. Alternatively, you can express the slope as $-6/1$, indicating a "rise" of $-6$ (downward) and a "run" of $1$ (rightward).

   Starting from $(0, 8)$:

   • Move 1 unit to the right ($x = 1$).
   • Move 6 units down ($y = 8 - 6 = 2$).
   • The second point is $(1, 2)$.

3. Plot the points and draw the line:

   • Plot $(0, 8)$ and $(1, 2)$ on the graph.
   • Draw a straight line through these two points to represent the equation $y = -6x + 8$.

Let me know if you'd like further clarification or additional questions!

Here are five related questions to deepen your understanding:

1. How can you determine the slope from a graph?
2. What does a negative slope signify about the direction of the line?
3. How would you graph a line with a slope of zero?
4. If the $y$-intercept were $-4$, how would the graph change?
5. How do you find the equation of a line from two points on the graph?

Tip: Always label the points you plot clearly to avoid confusion when drawing the line.