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Find the slope of the line of the points a=(-4,6) and b=(5,-4).

Mathematics

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Answers

2 parts
a

−38-\frac{3}{8}

b
-8

Step-by-step solution

6 steps

Here is the solution for finding the slope of the line for each pair of points.

The formula for the slope mm of a line passing through two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) is:

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

Part a· 3 steps

For the points (−4,6)(-4, 6) and (4,3)(4, 3)

  1. Assign the coordinates.

    Let (x1,y1)=(−4,6)(x_1, y_1) = (-4, 6)
    Let (x2,y2)=(4,3)(x_2, y_2) = (4, 3)

  2. Substitute the values into the slope formula.

    m=3−64−(−4)m = \frac{3 - 6}{4 - (-4)}

  3. Simplify the expression.

    m=−34+4m = \frac{-3}{4 + 4} m=−38m = \frac{-3}{8}

    The slope for part a) is −38\boxed{-\frac{3}{8}}.

Part b-8

For the points (5,4)(5, 4) and (6,−4)(6, -4)

  1. Assign the coordinates.

    Let (x1,y1)=(5,4)(x_1, y_1) = (5, 4)
    Let (x2,y2)=(6,−4)(x_2, y_2) = (6, -4)

  2. Substitute the values into the slope formula.

    m=−4−46−5m = \frac{-4 - 4}{6 - 5}

  3. Simplify the expression.

    m=−81m = \frac{-8}{1} m=−8m = -8

    The slope for part b) is −8\boxed{-8}.

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