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Math  /  Algebra

QuestionWhat is the slope of the line that passes through the points (−2,6)(-2,6) and (−12,2)(-12,2) Write your answer in simplest form.

Studdy Solution

STEP 1

1. We are given two points on a line: (−2,6)(-2, 6) and (−12,2)(-12, 2).
2. We need to find the slope of the line passing through these points.
3. The slope of a line 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 m = \frac{y_2 - y_1}{x_2 - x_1} .

STEP 2

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

STEP 3

Identify the coordinates of the two points.
The coordinates of the first point are (x1,y1)=(−2,6)(x_1, y_1) = (-2, 6).
The coordinates of the second point are (x2,y2)=(−12,2)(x_2, y_2) = (-12, 2).

STEP 4

Substitute the coordinates into the slope formula.
The slope m m is given by:
m=y2−y1x2−x1=2−6−12−(−2) m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - 6}{-12 - (-2)}

STEP 5

Simplify the expression to find the slope.
Calculate the differences in the numerator and the denominator:
m=2−6−12+2=−4−10 m = \frac{2 - 6}{-12 + 2} = \frac{-4}{-10}
Simplify the fraction:
m=−4−10=25 m = \frac{-4}{-10} = \frac{2}{5}
The slope of the line is:
25 \boxed{\frac{2}{5}}

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