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Math  /  Geometry

Question6. (6,5)(6,5) and (−2,1)(-2,1) m=\mathrm{m}=

Studdy Solution

STEP 1

1. We are given two points, (6,5) (6,5) and (−2,1) (-2,1) .
2. We need to find the slope (m \mathrm{m} ) of the line passing through these points.

STEP 2

1. Recall the formula for the slope of a line.
2. Substitute the given points into the formula.
3. Simplify to find the slope.

STEP 3

Recall that the slope m \mathrm{m} of a line passing through two points (x1,y1) (x_1, y_1) and (x2,y2) (x_2, y_2) is given by the formula:
m=y2−y1x2−x1\mathrm{m} = \frac{y_2 - y_1}{x_2 - x_1}

STEP 4

Substitute the coordinates of the given points (6,5) (6,5) and (−2,1) (-2,1) into the slope formula. Assign (x1,y1)=(6,5) (x_1, y_1) = (6, 5) and (x2,y2)=(−2,1) (x_2, y_2) = (-2, 1) .
m=1−5−2−6\mathrm{m} = \frac{1 - 5}{-2 - 6}

STEP 5

Calculate the differences in the numerator and the denominator:
1−5=−41 - 5 = -4 −2−6=−8-2 - 6 = -8

STEP 6

Substitute these values back into the formula:
m=−4−8\mathrm{m} = \frac{-4}{-8}

STEP 7

Simplify the fraction:
m=−4−8=12\mathrm{m} = \frac{-4}{-8} = \frac{1}{2}
The slope (m \mathrm{m} ) of the line passing through the points (6,5) (6,5) and (−2,1) (-2,1) is:
12 \boxed{\frac{1}{2}}

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