Determine the Position of Point C Relative to Line AB

Consider the points A(2, 3), B(6, 7), and C(2, 7) in a coordinate plane. You are asked to find the equation of the line that passes through points A and B and determine the position of point C relative to this line. Is point C above, below, or on the line?

The equation of the line through points A and B can be found using the two-point form of a line equation:

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

where $$ m $$ is the slope of the line calculated as:

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