https://file.aiquickdraw.com/mathbot/file/1727419265369awlsn41o.jpg

The equation provided in the image is:

\[
x - 2y = 4
\]

To graph this linear equation using intercepts, let's follow these steps:

### 1. Find the **x-intercept**:
The x-intercept occurs when \( y = 0 \). Substituting \( y = 0 \) into the equation:

\[
x - 2(0) = 4 \quad \Rightarrow \quad x = 4
\]

Thus, the x-intercept is \( (4, 0) \).

### 2. Find the **y-intercept**:
The y-intercept occurs when \( x = 0 \). Substituting \( x = 0 \) into the equation:

\[
0 - 2y = 4 \quad \Rightarrow \quad y = -2
\]

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

### 3. Plot the points:
- Plot the x-intercept \( (4, 0) \) on the graph.
- Plot the y-intercept \( (0, -2) \) on the graph.

### 4. Draw the line:
Using the two points \( (4, 0) \) and \( (0, -2) \), draw a straight line through them. This line represents the graph of the equation \( x - 2y = 4 \).

Would you like a detailed explanation on how to handle any part of this, or do you have specific questions about it?

### Questions for Further Exploration:
1. How do we verify if a point lies on the graph of the equation?
2. What is the slope of the line from the equation \( x - 2y = 4 \)?
3. Can we rewrite the equation in slope-intercept form? How does it help in graphing?
4. How does the graph change if the equation is altered to \( x - 2y = 6 \)?
5. How do we graph equations that are not in standard linear form?

### Tip:
When graphing linear equations, using both the x- and y-intercepts is a quick and efficient method to plot the line.

Use intercepts and a checkpoint to graph the linear function x - 2y = 4.

Learn how to graph the linear equation x - 2y = 4 by finding the x and y intercepts and drawing the graph through these points. This problem covers algebraic graphing methods, suitable for Grades 8-10.

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