To find the x-intercept and y-intercept of the equation $3x - 8y = 9$, follow these steps:

1. Finding the x-intercept:

• The x-intercept occurs when $y = 0$.
• Substituting $y = 0$ into the equation: $3x - 8(0) = 9 \quad \Rightarrow \quad 3x = 9 \quad \Rightarrow \quad x = \frac{9}{3} = 3$
• So, the x-intercept is $(3, 0)$.

2. Finding the y-intercept:

• The y-intercept occurs when $x = 0$.
• Substituting $x = 0$ into the equation: $3(0) - 8y = 9 \quad \Rightarrow \quad -8y = 9 \quad \Rightarrow \quad y = \frac{9}{-8} = -\frac{9}{8}$
• So, the y-intercept is $\left( 0, -\frac{9}{8} \right)$.

Intercepts:

• x-intercept: $(3, 0)$
• y-intercept: $\left( 0, -\frac{9}{8} \right)$

Would you like more details on intercepts or any other clarifications?

Here are some related questions for further exploration:

1. How do you find the slope of the line from the equation $3x - 8y = 9$?
2. What is the graphical significance of x-intercepts and y-intercepts?
3. How do you convert $3x - 8y = 9$ into slope-intercept form?
4. What happens if you adjust the constants in the equation, e.g., changing 9 to 12?
5. Can there be cases where an equation has no x-intercept or y-intercept?

Tip: To easily find intercepts, remember that setting one variable to 0 gives you the intercept for the other.