10.0 Gradient of a Straight Line

Master the gradient of a straight line! Learn to calculate slope, identify intercepts & more.

10.1 Gradient Gradient is the ratio of the vertical distance to the horizontal distance. The steepness of a straight line is determined by its gradient value. The greater the gradient value, the steeper the slope of the straight line. Line that has a steeper gradient has a greater angle. The negative or positive gradient value determines the direction of the slope of the straight line. Gradient of a straight line represents by letter m. 1. Determine the vertical distance and the horizontal distance of point P and point Q. Vertical distance 4 m 12 m 16 m Horizontal distance 6 m 3 m 2 m 2. Determine the vertical distance and the horizontal distance of line AB, CD and PQ in the following Cartesian plane. Line Vertical distance Horizontal distance (a) AB 3 units 3 units (b) CD 8 units 1 unit (c) PQ 6 units 4 units 3. Calculate the vertical distance and horizontal distance between P and Q in the diagram if the distance of each stair is 12cm. Vertical distance = 36cmHorizontal distance = 36cm 4. State the vertical distance and horizontal distance of the two pairs of points given.(a) (3, 0) and (−2, 6) Vertical distance= 6-0= 6unitsHorizontal distance= 3-(-2)= 5units (b) (1, 1) and (6, 5) Vertical distance= 5-1= 4unitsHorizontal distance= 6-1= 5units (c) (3, 6) and (6, −3) Vertical distance= 6-(-3)= 9unitsHorizontal distance= 6-3= 3units 5. State the value of the x-intercept and the value of the y-intercept of the straight line AB. No. The value of x-intercept The value of the y-intercept (a) 8 4 (b) 3 -7 (c) -5 3 (d) -1 -2 6. Identify the straight line that has the highest gradient in each of the diagrams below. AB CD EF AB CD EF 7. Based on the diagram, state whether the gradient is positive or negative. Positive MN Negative LM NO OQ