The problem is asking for the $x$- and $y$-intercepts of the equation:

$8y - 9x = -12$

Steps to Solve:

1. Find the $x$-intercept:

   • Set $y = 0$ and solve for $x$: $8(0) - 9x = -12$ $-9x = -12 \quad \implies \quad x = \frac{-12}{-9} = \frac{4}{3}$
   • The $x$-intercept is $\left( \frac{4}{3}, 0 \right)$.

2. Find the $y$-intercept:

   • Set $x = 0$ and solve for $y$: $8y - 9(0) = -12$ $8y = -12 \quad \implies \quad y = \frac{-12}{8} = -\frac{3}{2}$
   • The $y$-intercept is $\left( 0, -\frac{3}{2} \right)$.

Final Answer:

• $x$-intercept: $\left( \frac{4}{3}, 0 \right)$
• $y$-intercept: $\left( 0, -\frac{3}{2} \right)$

Would you like further details or a step-by-step breakdown?

Here are 5 related questions to explore:

1. How do you graph an equation using intercepts?
2. What does the slope of this line tell us about its steepness?
3. How can you rewrite the equation in slope-intercept form?
4. How do parallel and perpendicular lines relate to this equation?
5. What are other methods to find intercepts for linear equations?

Tip: Always verify intercepts by substituting them back into the original equation.