Graph the linear equation.

3y - 9x = -27

To graph the given linear equation, we will follow these steps:

1. **Rearrange the equation into slope-intercept form** \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

Starting with the equation:
\[
3y - 9x = -27
\]

### Step 1: Solve for \( y \)
\[
3y = 9x - 27
\]

Divide both sides by 3:
\[
y = 3x - 9
\]

Now, the equation is in slope-intercept form \( y = mx + b \), where:
- The slope \( m = 3 \)
- The y-intercept \( b = -9 \)

### Step 2: Plot the y-intercept
The y-intercept is \( -9 \), so we can plot the point \( (0, -9) \) on the y-axis.

### Step 3: Use the slope
The slope \( m = 3 \) means that for every 1 unit you move to the right along the x-axis, you move up 3 units. So, from the point \( (0, -9) \), move right by 1 and up by 3 to plot the next point, \( (1, -6) \).

### Step 4: Draw the line
Once you have two points, \( (0, -9) \) and \( (1, -6) \), draw a straight line through them to represent the linear equation.

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If you'd like, I can graph this equation for you visually. Would you like that?

Here are 5 questions related to graphing and linear equations:
1. How do you find the slope of a line from its equation?
2. What is the significance of the y-intercept in a graph?
3. Can a linear equation have more than one solution?
4. How can you verify if a point lies on a given line?
5. What does the slope represent in real-world applications?

**Tip**: When graphing, always start by identifying key points like the intercepts and use the slope to plot additional points efficiently!

Learn how to graph the linear equation 3y - 9x = -27. This detailed guide walks through solving the equation for y, finding the slope and y-intercept, and plotting the graph. Perfect for students in Grades 8-10 learning algebra and graphing techniques.

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