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Find the gradient of the line passing through the points P(1, -1/2) and Q(3, -8 1/2).

Mathematics

ScanSolve AI Answer

Answer

-4

Step-by-step solution

7 steps

  1. Identify the coordinates of the two given points.

    The points are P(x1,y1)=(1,−12)P(x_1, y_1) = (1, -\frac{1}{2}) and Q(x2,y2)=(3,−812)Q(x_2, y_2) = (3, -8\frac{1}{2}).

  2. Convert the mixed fraction to an improper fraction.

    y2=−812=−(8×2)+12=−16+12=−172y_2 = -8\frac{1}{2} = -\frac{(8 \times 2) + 1}{2} = -\frac{16 + 1}{2} = -\frac{17}{2}.

  3. Use the formula for the gradient (slope) of a line passing through two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2)

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

  4. Substitute the coordinates into the formula.

    m=−172−(−12)3−1m = \frac{-\frac{17}{2} - (-\frac{1}{2})}{3 - 1}

  5. Simplify the numerator.

    −172−(−12)=−172+12=−17+12=−162=−8-\frac{17}{2} - (-\frac{1}{2}) = -\frac{17}{2} + \frac{1}{2} = \frac{-17 + 1}{2} = \frac{-16}{2} = -8

  6. Simplify the denominator.

    3−1=23 - 1 = 2

  7. Calculate the gradient.

    m=−82=−4m = \frac{-8}{2} = -4

    The gradient of the line passing through points P and Q is:

    −4-4
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