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!