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Math  /  Algebra

QuestionFind the slope of the line passing through the given points. (−4,4),(−6,10)(-4,4),(-6,10)
The slope of the line is □\square 16 (Type an integer or a simplified fraction.)

Studdy Solution

STEP 1

1. The slope of a line passing through two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) is calculated using the slope formula.
2. The formula for the slope m m is given by 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 given points: - The first point is (−4,4)(-4, 4), so x1=−4 x_1 = -4 and y1=4 y_1 = 4 . - The second point is (−6,10)(-6, 10), so x2=−6 x_2 = -6 and y2=10 y_2 = 10 .

STEP 4

Substitute the coordinates into the slope formula:
m=y2−y1x2−x1=10−4−6−(−4) m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{10 - 4}{-6 - (-4)}

STEP 5

Simplify the expression:
m=10−4−6+4=6−2 m = \frac{10 - 4}{-6 + 4} = \frac{6}{-2}

STEP 6

Further simplify the fraction:
m=−3 m = -3

STEP 7

The slope of the line passing through the points (−4,4)(-4, 4) and (−6,10)(-6, 10) is:
−3 \boxed{-3}

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