To graph the equation $3x + 9y = 27$ using the x- and y-intercepts, follow these steps:

1. Find the x-intercept: Set $y = 0$ in the equation: $3x + 9(0) = 27 \implies 3x = 27 \implies x = 9$ So, the x-intercept is $(9, 0)$.

2. Find the y-intercept: Set $x = 0$ in the equation: $3(0) + 9y = 27 \implies 9y = 27 \implies y = 3$ So, the y-intercept is $(0, 3)$.

3. Plot the intercepts:

   • Plot the point $(9, 0)$ on the x-axis.
   • Plot the point $(0, 3)$ on the y-axis.

4. Draw the line: Connect the two points with a straight line, which represents the graph of the equation.

Summary of Intercepts:

• x-intercept: $(9, 0)$
• y-intercept: $(0, 3)$

Would you like more details on this process or have any specific questions? Here are some related questions you might consider:

1. How do you find the slope of the line from the equation?
2. What would be the equation in slope-intercept form?
3. How can you identify whether the line is increasing or decreasing?
4. How do you graph another linear equation using a different method?
5. What are the implications of intercepts in real-world scenarios?

Tip: Always check if the equation can be simplified before finding intercepts, as this can sometimes make calculations easier!