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Math  /  Algebra

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What is the slope of the line that passes through the points (10,4)(10,4) and (7,3)(7,3) ? Write your answer in simplest form.

Studdy Solution

STEP 1

1. We are given two points: (10,4) (10, 4) and (7,3) (7, 3) .
2. We need to find the slope of the line passing through these points.
3. The slope formula is used to calculate the slope between two points.

STEP 2

1. Recall the slope formula.
2. Substitute the given points into the slope formula.
3. Simplify the expression to find the slope.

STEP 3

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

STEP 4

Substitute the given points (10,4) (10, 4) and (7,3) (7, 3) into the slope formula. Assign (x1,y1)=(10,4) (x_1, y_1) = (10, 4) and (x2,y2)=(7,3) (x_2, y_2) = (7, 3) .
m=3−47−10 m = \frac{3 - 4}{7 - 10}

STEP 5

Simplify the expression to find the slope.
m=−1−3 m = \frac{-1}{-3}
Since dividing two negative numbers results in a positive number:
m=13 m = \frac{1}{3}
The slope of the line is:
13 \boxed{\frac{1}{3}}

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