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The problem states that triangle ABC has vertex A on the y-axis, and the equation of line AB is given as:

\[
7y - 6x - 21 = 0
\]

We are asked to find the coordinates of point A, which lies on the y-axis. 

Since point A lies on the y-axis, its x-coordinate must be 0. To find the y-coordinate of A, we substitute \(x = 0\) into the equation of the line AB and solve for \(y\):

\[
7y - 6(0) - 21 = 0
\]

Simplifying:

\[
7y - 21 = 0
\]

\[
7y = 21
\]

\[
y = \frac{21}{7} = 3
\]

Thus, the coordinates of point A are:

\[
(0, 3)
\]

Would you like more details on this, or do you have any further questions?

### Related Questions:
1. How do you find the equation of a line passing through two points?
2. What is the slope of the line AB from the given equation?
3. Can you explain the significance of the y-intercept for a line?
4. How can we find the intersection of two lines algebraically?
5. What is the geometric interpretation of the equation \(7y - 6x - 21 = 0\)?

**Tip:** When a point lies on the y-axis, its x-coordinate is always zero.

The triangle ABC has vertex A on the y-axis. The equation of AB is 7y - 6x - 21 = 0. State the coordinates of A.

This problem explores how to find the coordinates of a point lying on the y-axis, given the equation of a line. The equation of the line AB is 7y - 6x - 21 = 0, and we will determine the coordinates of point A using the properties of lines and the y-axis. Suitable for students in Grades 9-10.

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