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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.

Graph the following equation by rewriting the equation of the line in slope intercept form: 4x - y = 8

Learn how to graph the linear equation 4x - y = 8 by rewriting it in slope-intercept form (y = 4x - 8). This step-by-step solution covers algebraic concepts such as slope and y-intercept, suitable for students in Grades 8-10.

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