To determine the $x$- and $y$-intercepts of the equation $6x - 2y = -18$:

Step 1: Find the $x$-intercept

The $x$-intercept occurs when $y = 0$. Substitute $y = 0$ into the equation: $6x - 2(0) = -18$ $6x = -18$ $x = -3$ Thus, the $x$-intercept is $(-3, 0)$.

Step 2: Find the $y$-intercept

The $y$-intercept occurs when $x = 0$. Substitute $x = 0$ into the equation: $6(0) - 2y = -18$ $-2y = -18$ $y = 9$ Thus, the $y$-intercept is $(0, 9)$.

Final Answer:

The $x$- and $y$-intercepts are: \text{x-intercept: } (-3, 0), \text{y-intercept: } (0, 9) From the choices given in the image, the correct answer is (b).

Would you like further clarification or a detailed breakdown of the steps? Here are five related questions to expand your understanding:

1. How do intercepts help in graphing linear equations?
2. Can you explain how to rewrite an equation in slope-intercept form?
3. How would you find intercepts for a quadratic equation?
4. What is the significance of the intercepts in real-world problems?
5. How do intercepts relate to parallel and perpendicular lines?

Tip: Always double-check by substituting intercept values back into the equation to verify their correctness!