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Find the gradients of the line joining the following pairs of points: a) (2,5) and (4,8) b) (-3,2) and (4,4)

Mathematics

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2 parts
b
2
c
2

Step-by-step solution

6 steps

Part b· 3 steps

  1. The formula for the gradient mm of a line passing through two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) is

    m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}

  2. The points are (x1,y1)=(2,3)(x_1, y_1) = (2, 3) and (x2,y2)=(4,7)(x_2, y_2) = (4, 7).

    Substitute the values:

    m=7−34−2m = \frac{7 - 3}{4 - 2}

  3. Simplify

    m=42=2m = \frac{4}{2} = 2

    The gradient is 2\boxed{2}.

Part c2

  1. The formula for the gradient mm of a line passing through two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) is

    m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}

  2. The points are (x1,y1)=(3,5)(x_1, y_1) = (3, 5) and (x2,y2)=(6,11)(x_2, y_2) = (6, 11).

    Substitute the values:

    m=11−56−3m = \frac{11 - 5}{6 - 3}

  3. Simplify

    m=63=2m = \frac{6}{3} = 2

    The gradient is 2\boxed{2}.

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