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Determine the equation of the line through the points (-1, -7) and (-2, -5).

Mathematics

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y=−2x−9y = -2x - 9

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2.a) Determine the equation of the line through the points (−1,−7)(-1, -7) and (−2,−5)(-2, -5).

  1. Calculate the gradient mm using the formula m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}.

    Let (x1,y1)=(−1,−7)(x_1, y_1) = (-1, -7) and (x2,y2)=(−2,−5)(x_2, y_2) = (-2, -5).

    m=−5−(−7)−2−(−1)m = \frac{-5 - (-7)}{-2 - (-1)} m=−5+7−2+1m = \frac{-5 + 7}{-2 + 1} m=2−1m = \frac{2}{-1} m=−2m = -2

  2. Use the point-slope form y−y1=m(x−x1)y - y_1 = m(x - x_1) with m=−2m = -2 and point (−1,−7)(-1, -7).

    y−(−7)=−2(x−(−1))y - (-7) = -2(x - (-1)) y+7=−2(x+1)y + 7 = -2(x + 1)

  3. Distribute the gradient and solve for yy.

    y+7=−2x−2y + 7 = -2x - 2 y=−2x−2−7y = -2x - 2 - 7 y=−2x−9y = -2x - 9
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