Questions: Find the slope of the line passing through the points (-3,7) and (2,-6).

Find the slope of the line passing through the points (-3,7) and (2,-6).
Transcript text: Find the slope of the line passing through the points $(-3,7)$ and $(2,-6)$. $\square$
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Solution

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Solution Steps

To find the slope of the line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\), we use the formula: \[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \] We will substitute the given points \((-3, 7)\) and \((2, -6)\) into this formula to find the slope.

Step 1: Identify the given points

We are given two points: \((-3, 7)\) and \((2, -6)\).

Step 2: Use the slope formula

The formula for the slope \( m \) of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) is: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Step 3: Substitute the given points into the formula

Substitute \((x_1, y_1) = (-3, 7)\) and \((x_2, y_2) = (2, -6)\) into the formula: \[ m = \frac{-6 - 7}{2 - (-3)} \]

Step 4: Simplify the expression

Simplify the numerator and the denominator: \[ m = \frac{-13}{5} \]

Final Answer

The slope of the line passing through the points \((-3, 7)\) and \((2, -6)\) is: \[ \boxed{m = -2.6} \]

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