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Find the gradient of the line joining the points A(3,4) and B(9,16).

Mathematics

ScanSolve AI Answer

Answer

2\text{2}

Step-by-step solution

3 steps

Here's how to determine the gradient of the line:

  1. Identify the coordinates of the two points.

    The given points are A(3,4)A(3,4) and B(9,16)B(9,16).
    Let (x1,y1)=(3,4)(x_1, y_1) = (3, 4) and (x2,y2)=(9,16)(x_2, y_2) = (9, 16).

  2. Use the formula for the gradient (slope) of a line.

    The gradient mm is given by the formula:

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

  3. Substitute the coordinates into the formula and calculate.

    m=16−49−3m = \frac{16 - 4}{9 - 3} m=126m = \frac{12}{6} m=2m = 2

    The gradient of the straight line joining the two points is 2\text{2}.

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