Line Segment Equation in Coordinate Geometry

Consider the following points in a coordinate plane: A(2, 3), B(5, 7), and C(x, y). If point C lies on the line segment joining points A and B, which of the following equations represents the relationship between x and y for point C?

To find the equation of the line segment AB, use the formula for the slope between two points, given by:

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

Then, apply the point-slope form of the equation:

$$ y - y_1 = m(x - x_1) $$

Substitute A's coordinates to find the linear equation on which point C lies.