Problem:

We are tasked to find the x-intercept and y-intercept for the equation $3x - 5y = 30$.

Solution:

1. Find the x-intercept:

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

$3x - 5(0) = 30$

$3x = 30$

$x = \frac{30}{3} = 10$

Thus, the x-intercept is $(10, 0)$.

2. Find the y-intercept:

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

$3(0) - 5y = 30$

$-5y = 30$

$y = \frac{30}{-5} = -6$

Thus, the y-intercept is $(0, -6)$.

Final Answer:

• x-intercept: $(10, 0)$
• y-intercept: $(0, -6)$

Let me know if you'd like further explanation or details!

Related Questions:

1. What is the slope of the line represented by $3x - 5y = 30$?
2. Rewrite $3x - 5y = 30$ in slope-intercept form ($y = mx + b$).
3. Determine if the line intersects the origin.
4. Solve for $y$ when $x = 4$.
5. What are the coordinates of the midpoint between the x- and y-intercepts?

Tip:

When finding intercepts, always substitute $y = 0$ for the x-intercept and $x = 0$ for the y-intercept.