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To graph the equation \( x - 4y = 8 \) using the intercepts, let's find the \( x \)- and \( y \)-intercepts and then plot the line through those points.

### Step 1: Find the \( x \)-intercept
The \( x \)-intercept occurs where \( y = 0 \).

1. Substitute \( y = 0 \) into the equation:
   \[
   x - 4(0) = 8
   \]
2. Simplify to find \( x \):
   \[
   x = 8
   \]

So, the \( x \)-intercept is at \( (8, 0) \).

### Step 2: Find the \( y \)-intercept
The \( y \)-intercept occurs where \( x = 0 \).

1. Substitute \( x = 0 \) into the equation:
   \[
   0 - 4y = 8
   \]
2. Solve for \( y \):
   \[
   -4y = 8 \Rightarrow y = -2
   \]

So, the \( y \)-intercept is at \( (0, -2) \).

### Step 3: Plot the Intercepts and Draw the Line
On the graph:
- Plot the point \( (8, 0) \) on the \( x \)-axis.
- Plot the point \( (0, -2) \) on the \( y \)-axis.
- Draw a straight line passing through these two points to represent the equation \( x - 4y = 8 \).

Would you like additional details on how this line is derived, or any assistance with other questions?

Here are five related questions to deepen your understanding:
1. How would you rewrite the equation \( x - 4y = 8 \) in slope-intercept form?
2. What would the graph look like if the equation were \( x + 4y = 8 \)?
3. How do you interpret the slope of the line from the equation \( x - 4y = 8 \)?
4. How can you verify the intercepts algebraically?
5. What would be the effect on the intercepts if the equation were \( 2x - 8y = 16 \)?

**Tip:** When finding intercepts, always set the opposite variable to zero, as intercepts are the points where the line crosses each axis.

Use the intercepts to graph the equation x - 4y = 8.

Learn how to graph the linear equation x - 4y = 8 using intercepts. This step-by-step solution covers how to find the x- and y-intercepts, plot them on a graph, and draw the line. Perfect for students in Grades 9-10.

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