Q.Find the value of k if the point P(1,k) lies on the line passing through the points A(2, 2) and B(3, 3).

The slope of a line is the tangent of its inclination — the angle θ the line makes with the positive X-axis, measured anticlockwise, with 0° ≤ θ < 180°. So slope m = tanθ. Equivalently, for any two points on a non-vertical line, the slope equals the change in y divided by the change in x between them. A horizontal line has slope 0 (inclination 0°); a vertical line has undefined slope (inclination 90°, where tangent is undefined). Two lines are parallel exactly when they share the same slope, and two non-vertical lines are perpendicular exactly when the product of their slopes is −1 — a fact proved by relating the two lines' inclinations and using the tangent-difference identity. This single number, the slope, packages a line's steepness and direction, and drives almost every later construction in the chapter: finding equations of lines, altitudes, perpendicular bisectors, medians, and testing whether three points are collinear (three points are collinear exactly when the slope between any two pairs of them is the same).