The equation given is $3x + 5y = 30$. We need to find both the x-intercept and the y-intercept.

1. X-intercept:

The x-intercept occurs when $y = 0$. Substituting $y = 0$ into the equation:

$3x + 5(0) = 30 \implies 3x = 30 \implies x = \frac{30}{3} = 10$

Thus, the x-intercept is $x = 10$, which is already provided in the image.

2. Y-intercept:

The y-intercept occurs when $x = 0$. Substituting $x = 0$ into the equation:

$3(0) + 5y = 30 \implies 5y = 30 \implies y = \frac{30}{5} = 6$

Thus, the y-intercept is $y = 6$.

Would you like more details on this? Here are some related questions for further exploration:

1. What is the geometric meaning of the x- and y-intercepts?
2. How would you graph the line using the intercepts?
3. Can you rewrite the equation in slope-intercept form?
4. What is the slope of the line in this equation?
5. How would the intercepts change if the constants in the equation were different?

Tip: When solving for intercepts, remember that at the x-intercept, $y = 0$, and at the y-intercept, $x = 0$.