Graph the equation using the slope and the​ y-intercept.
x minus 2 y equals 12

To graph the equation \( x - 2y = 12 \), we first need to rewrite it in slope-intercept form, \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

### Step 1: Rewrite the equation
Start with the original equation:
\[
x - 2y = 12
\]

Solve for \( y \):
1. Subtract \( x \) from both sides:
   \[
   -2y = -x + 12
   \]

2. Divide each term by -2:
   \[
   y = \frac{x}{2} - 6
   \]

Now, the equation is in slope-intercept form: 
\[
y = \frac{1}{2}x - 6
\]
Here, the slope \( m \) is \( \frac{1}{2} \), and the y-intercept \( b \) is -6.

### Step 2: Graph the equation
1. **Plot the y-intercept**: Start by plotting the point (0, -6) on the graph.
2. **Use the slope**: The slope \( \frac{1}{2} \) means you rise 1 unit up for every 2 units you move to the right. From the point (0, -6), move up 1 unit and 2 units to the right to get the next point (2, -5).
3. **Draw the line**: Connect these points to form a straight line.

Would you like a visual representation of this graph? Let me know if you have any questions or want more details.

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### Related Questions:
1. How do you find the slope from a standard form equation like \( Ax + By = C \)?
2. What is the significance of the y-intercept in a graph?
3. How does the slope of a line affect its steepness?
4. How would you graph an equation with a negative slope?
5. How can you convert an equation from slope-intercept form back to standard form?

**Tip:** When converting from standard form \( Ax + By = C \) to slope-intercept form, always isolate the \( y \)-term by solving step-by-step.

Learn how to graph the linear equation x - 2y = 12 by converting it to slope-intercept form. Follow a step-by-step guide to determine the slope and y-intercept, then use them to plot the line. Ideal for students in Grades 8-10.

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