To find the $y$-intercept of the equation $3y - 10x = 1$, we set $x = 0$ because the $y$-intercept occurs where the line crosses the $y$-axis, and at this point, $x = 0$.

Steps:

1. Substitute $x = 0$ into the equation: $3y - 10(0) = 1$ This simplifies to: $3y = 1$

2. Solve for $y$: $y = \frac{1}{3}$

Conclusion:

The $y$-intercept is $\frac{1}{3}$. This can be written as the point: $(0, \frac{1}{3})$

Would you like details or have questions? Here are related queries:

1. How do you find the $x$-intercept for the same equation?
2. Can you rewrite this equation in slope-intercept form $y = mx + b$?
3. What does the slope of this line represent geometrically?
4. How do you graph this equation starting with the intercepts?
5. What are parallel lines to this equation in standard form?

Tip: Always set $x = 0$ for $y$-intercept and $y = 0$ for $x$-intercept when working with linear equations.