To rewrite the given equation $4x - y = 8$ in slope-intercept form (which is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept), we need to solve for $y$.

Starting with the given equation: $4x - y = 8$

1. Subtract $4x$ from both sides: $-y = -4x + 8$

2. Multiply both sides by $-1$ to solve for $y$: $y = 4x - 8$

Now, the equation is in slope-intercept form: $y = 4x - 8$

This means the slope $m$ is 4, and the y-intercept $b$ is $-8$.

To graph this line, follow these steps:

1. Plot the y-intercept $(0, -8)$ on the coordinate plane.
2. Use the slope to find another point on the line. The slope of 4 means that for every 1 unit you move to the right on the x-axis, you move 4 units up on the y-axis. So from $(0, -8)$, move right 1 unit to $x = 1$ and up 4 units to $y = -4$. This gives you the point $(1, -4)$.
3. Draw a line through the points $(0, -8)$ and $(1, -4)$.

Would you like more details on graphing this equation, or do you have any other questions? Here are some related questions for further exploration:

1. How do you determine the x-intercept of the line $4x - y = 8$?
2. What is the significance of the slope in the context of a real-world problem?
3. How can you convert the slope-intercept form back to the standard form?
4. What are the differences between standard form and slope-intercept form?
5. Can you provide examples of parallel and perpendicular lines to $y = 4x - 8$?

Tip: When graphing lines, always identify and plot the intercepts first for an accurate graph.