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Calculate the slope m using the given points (x1, y1) = (8, 4) and (x2, y2) = (-12, -3).

Mathematics

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Answer

7x−20y+24=07x - 20y + 24 = 0

Step-by-step solution

3 steps

  1. Calculate the slope mm using the given points (x1,y1)=(8,4)(x_1, y_1) = (8, 4) and (x2,y2)=(−12,−3)(x_2, y_2) = (-12, -3).

    m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1} m=−3−4−12−8m = \frac{-3 - 4}{-12 - 8} m=−7−20m = \frac{-7}{-20} m=720m = \frac{7}{20}

  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 (e.g., (8,4)(8, 4)) and the calculated slope m=720m = \frac{7}{20}.

    y−4=720(x−8)y - 4 = \frac{7}{20}(x - 8)

  3. Convert the equation to the standard form Ax+By+C=0Ax + By + C = 0.

    Multiply both sides by 20 to eliminate the fraction:

    20(y−4)=7(x−8)20(y - 4) = 7(x - 8) 20y−80=7x−5620y - 80 = 7x - 56

    Rearrange the terms to one side:

    0=7x−20y−56+800 = 7x - 20y - 56 + 80 7x−20y+24=07x - 20y + 24 = 0
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