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Find the equation of the line passing through the points (2,4) and (5,13).

Mathematics

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Answer

y = 3x - 2\text{y = 3x - 2}

Step-by-step solution

3 steps

I will solve question 8.

  1. Calculate the gradient (mm) of the line passing through points A(2,4)A(2,4) and B(5,13)B(5,13).

    The formula for the gradient is m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}.
    Given points A(x1,y1)=(2,4)A(x_1, y_1) = (2,4) and B(x2,y2)=(5,13)B(x_2, y_2) = (5,13).

    m=13−45−2=93=3m = \frac{13 - 4}{5 - 2} = \frac{9}{3} = 3

  2. Use the point-slope form of a linear equation, y−y1=m(x−x1)y - y_1 = m(x - x_1), with one of the points and the calculated gradient.

    Using point A(2,4)A(2,4) and m=3m=3:

    y−4=3(x−2)y - 4 = 3(x - 2)

  3. Convert the equation to the form y=mx+cy = mx + c.

    y−4=3x−6y - 4 = 3x - 6 y=3x−6+4y = 3x - 6 + 4 y=3x−2y = 3x - 2
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