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To graph the equation \( x - 2y = 6 \) using intercepts, we’ll find the points where the line intersects the x-axis and y-axis.

### Step 1: Rewrite in Standard Form
The equation is already in standard form:
\[
x - 2y = 6
\]

### Step 2: Find the x-intercept
To find the x-intercept, set \( y = 0 \) in the equation:
\[
x - 2(0) = 6 \Rightarrow x = 6
\]
So, the x-intercept is \( (6, 0) \).

### Step 3: Find the y-intercept
To find the y-intercept, set \( x = 0 \) in the equation:
\[
0 - 2y = 6 \Rightarrow y = -3
\]
So, the y-intercept is \( (0, -3) \).

### Step 4: Plot the Points and Draw the Line
1. Plot the point \( (6, 0) \) on the x-axis.
2. Plot the point \( (0, -3) \) on the y-axis.
3. Draw a straight line through these points to complete the graph.

Would you like further details or have any questions?

### Related Questions
1. How would you find the slope of the line from this equation?
2. What would be the slope-intercept form of the equation \( x - 2y = 6 \)?
3. If you changed the equation to \( x - 2y = 4 \), how would the intercepts change?
4. How do you determine if two lines are parallel based on their equations?
5. What is the relationship between the standard form and slope-intercept form of a line?

### Tip
When graphing a line, using intercepts is quick and efficient, especially for lines in standard form like \( Ax + By = C \).

Graph the equation x - 2y = 6 using the intercept form.

Learn how to graph the linear equation x - 2y = 6 by finding the x- and y-intercepts. This guide explains each step, including calculating intercepts and plotting points on the coordinate plane. Suitable for students in Grades 8-10.

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