To graph the line $9x - y = -9$ using intercepts, let's find both the x-intercept and the y-intercept.

1. Finding the x-intercept

The x-intercept occurs when $y = 0$. Substitute $y = 0$ in the equation:

$9x - 0 = -9 \implies 9x = -9 \implies x = -1$

So, the x-intercept is at $(-1, 0)$.

2. Finding the y-intercept

The y-intercept occurs when $x = 0$. Substitute $x = 0$ in the equation:

$9(0) - y = -9 \implies -y = -9 \implies y = 9$

So, the y-intercept is at $(0, 9)$.

Plotting the Points and Drawing the Line

1. Plot the point $(-1, 0)$ on the x-axis.
2. Plot the point $(0, 9)$ on the y-axis.
3. Draw a line through these two points to represent the equation $9x - y = -9$.

This line should now be correctly positioned on the graph.

Would you like additional details, or do you have any questions?

Here are 5 related questions to explore further:

1. How would you find the slope of the line from the equation $9x - y = -9$?
2. What happens to the graph if the equation changes to $9x - y = 9$?
3. How can you verify if a point lies on the line $9x - y = -9$?
4. How would you rewrite $9x - y = -9$ in slope-intercept form $y = mx + b$?
5. What is the general approach to finding intercepts for any linear equation in standard form?

Tip: For any line in standard form $Ax + By = C$, you can quickly find intercepts by setting $y = 0$ to find $x$ and $x = 0$ to find $y$.