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Math  /  Algebra

QuestionGive the slope between the points (−4,−2)(5,−13)(-4,-2) \quad(5,-13) OK

Studdy Solution

STEP 1

1. We are given two points: (−4,−2)(-4, -2) and (5,−13) (5, -13) .
2. The slope of a line through two points can be calculated using the slope formula.
3. The slope formula is m=y2−y1x2−x1 m = \frac{y_2 - y_1}{x_2 - x_1} .

STEP 2

1. Identify the coordinates of the given points.
2. Substitute the coordinates into the slope formula.
3. Simplify the expression to find the slope.

STEP 3

Identify the coordinates of the points:
Point 1: (−4,−2)(-4, -2) where x1=−4 x_1 = -4 and y1=−2 y_1 = -2
Point 2: (5,−13) (5, -13) where x2=5 x_2 = 5 and y2=−13 y_2 = -13

STEP 4

Substitute the coordinates into the slope formula:
m=y2−y1x2−x1=−13−(−2)5−(−4) m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-13 - (-2)}{5 - (-4)}

STEP 5

Simplify the expression:
m=−13+25+4 m = \frac{-13 + 2}{5 + 4}
m=−119 m = \frac{-11}{9}

STEP 6

The slope of the line through the points (−4,−2)(-4, -2) and (5,−13) (5, -13) is:
−119 \boxed{-\frac{11}{9}}

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