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.