Finding Y-Coordinate in Coordinate Geometry

In the coordinate plane, point A is located at (2, 3) and point B is located at (10, 7). A third point C lies on the line that passes through points A and B. If the x-coordinate of point C is 6, what is the y-coordinate of point C?

To find the y-coordinate, first determine the slope of line AB. The slope $m$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by the formula:

$m = \f\frac{y_2 - y_1}{x_2 - x_1}$

Use this formula to calculate the slope and then apply point-slope form or the line equation to find the specific y-coordinate at $x = 6$.