Math / Geometry

QuestionWhat is the slope of the line that passes through the points $(2,-4)$ and $(5,2)$ ? Write your answer in simplest form.

Studdy Solution

STEP 1

1. The formula for the slope $m$ of a line passing through two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by: $ m = \frac{y_2 - y_1}{x_2 - x_1} \]
2. We are given the points $(2, -4)$ and $(5, 2)$.

STEP 2

1. Identify the coordinates of the 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. We have: - Point 1: $(x_1, y_1) = (2, -4)$ - Point 2: $(x_2, y_2) = (5, 2)$

STEP 4

Substitute the coordinates into the slope formula: $m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - (-4)}{5 - 2}$

STEP 5

Simplify the expression: $m = \frac{2 + 4}{5 - 2} = \frac{6}{3}$

STEP 6

Simplify the fraction to its simplest form: $m = \frac{6}{3} = 2$
The slope of the line that passes through the points $(2, -4)$ and $(5, 2)$ is:
$\boxed{2}$

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QuestionWhat is the slope of the line that passes through the points $(2,-4)$ and $(5,2)$ ? Write your answer in simplest form.

Studdy Solution

STEP 1

1. The formula for the slope $m$ of a line passing through two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by: $ m = \frac{y_2 - y_1}{x_2 - x_1} \]
2. We are given the points \((2, -4)\) and \((5, 2)\).

STEP 2

1. Identify the coordinates of the 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. We have: - Point 1: $(x_1, y_1) = (2, -4)$ - Point 2: $(x_2, y_2) = (5, 2)$

STEP 4

Substitute the coordinates into the slope formula: $m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - (-4)}{5 - 2}$

STEP 5

Simplify the expression: $m = \frac{2 + 4}{5 - 2} = \frac{6}{3}$

STEP 6

Simplify the fraction to its simplest form: $m = \frac{6}{3} = 2$
The slope of the line that passes through the points $(2, -4)$ and $(5, 2)$ is:
$\boxed{2}$

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QuestionWhat is the slope of the line that passes through the points (2,−4)(2,-4)(2,−4) and (5,2)(5,2)(5,2) ? Write your answer in simplest form.

Studdy Solution

STEP 1

1. The formula for the slope m m m of a line passing through two points (x1,y1)(x_1, y_1)(x1​,y1​) and (x2,y2)(x_2, y_2)(x2​,y2​) is given by: $ m = \frac{y_2 - y_1}{x_2 - x_1} \]2. We are given the points \((2, -4)\) and \((5, 2)\).

STEP 2

1. Identify the coordinates of the 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. We have: - Point 1: (x1,y1)=(2,−4)(x_1, y_1) = (2, -4)(x1​,y1​)=(2,−4) - Point 2: (x2,y2)=(5,2)(x_2, y_2) = (5, 2)(x2​,y2​)=(5,2)

STEP 4

Substitute the coordinates into the slope formula: m=y2−y1x2−x1=2−(−4)5−2m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - (-4)}{5 - 2}m=x2​−x1​y2​−y1​​=5−22−(−4)​

STEP 5

Simplify the expression: m=2+45−2=63m = \frac{2 + 4}{5 - 2} = \frac{6}{3}m=5−22+4​=36​

STEP 6

Simplify the fraction to its simplest form: m=63=2m = \frac{6}{3} = 2m=36​=2 The slope of the line that passes through the points (2,−4)(2, -4)(2,−4) and (5,2)(5, 2)(5,2) is:2 \boxed{2} 2​

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QuestionWhat is the slope of the line that passes through the points $(2,-4)$ and $(5,2)$ ? Write your answer in simplest form.

1. The formula for the slope $m$ of a line passing through two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by: $ m = \frac{y_2 - y_1}{x_2 - x_1} \]
2. We are given the points \((2, -4)\) and \((5, 2)\).

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

Identify the coordinates of the points. We have: - Point 1: $(x_1, y_1) = (2, -4)$ - Point 2: $(x_2, y_2) = (5, 2)$

Substitute the coordinates into the slope formula: $m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - (-4)}{5 - 2}$

Simplify the expression: $m = \frac{2 + 4}{5 - 2} = \frac{6}{3}$

Simplify the fraction to its simplest form: $m = \frac{6}{3} = 2$
The slope of the line that passes through the points $(2, -4)$ and $(5, 2)$ is:
$\boxed{2}$