Practice Maths

Gradient and Equation of a Line — Solutions

Click any answer to watch the solution video.

  1. Calculate gradients

    1. (1,3) and (3,7):
    2. (0,5) and (4,13):
    3. (2,8) and (6,4):
    4. (−1,2) and (3,10):
    5. (0,0) and (5,15):
    6. (−3,4) and (1,−4):
    7. (2,−1) and (2,6):
    8. (−4,3) and (2,3):
    9. (3,5) and (7,13):
    10. (−2,−5) and (4,7):

  2. Gradient types

    1. m = 4:
    2. m = −2:
    3. m = 0:
    4. Undefined:
    5. m = ½:
    6. m = −5:

  3. Equation from gradient and point

    1. m=2, (1,5):
    2. m=−3, (2,4):
    3. m=4, (0,−7):
    4. m=½, (4,3):
    5. m=−1, (−2,6):
    6. m=5, (3,0):
    7. m=−2, (0,8):
    8. m=¾, (4,5):

  4. Interpret gradient in context

    1. C = 12t + 25, gradient 12:
    2. Ramp gradient 0.15:
    3. Diver through (0,0) and (5,−20):
    4. Horizontal line through (0,4):

  5. Order by steepness

    1. Line A,B,C:
    2. Line P,Q,R:

  6. Problem solving

    1. Road gradient:
    2. Find k for m=2, (k,3) and (4,11):
    3. Gradient 3 through midpoint of (0,2) and (4,8):
    4. Vertical and horizontal through (5,−3):

  7. Equation from gradient and point

    1. m=2, (1,5):
    2. m=−3, (2,4):
    3. m=4, (0,−7):
    4. m=½, (4,3):
    5. m=−1, (−2,6):
    6. m=5, (3,0):

  8. Order by steepness

  9. Problem solving with gradient

  10. Equations in context