Questions: m=(y2-y1)/(x2-x1) so (6-2)/(-4-2)=-4/6

m=(y2-y1)/(x2-x1) so (6-2)/(-4-2)=-4/6
Transcript text: $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$ so $\frac{6-2}{-4-2}=-\frac{4}{2}$
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Solution

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Solution Steps

To find the slope \( m \) of a line given two points \((x_1, y_1)\) and \((x_2, y_2)\), use the formula \( m = \frac{y_2 - y_1}{x_2 - x_1} \). Substitute the given points into the formula to calculate the slope.

Step 1: Calculate the Slope

To find the slope \( m \) of the line passing through the points \((2, 2)\) and \((-4, 6)\), we use the formula:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Substituting the values:

\[ m = \frac{6 - 2}{-4 - 2} = \frac{4}{-6} = -\frac{2}{3} \approx -0.6667 \]

Step 2: Interpret the Result

The calculated slope \( m = -0.6667 \) indicates that for every unit increase in \( x \), the value of \( y \) decreases by approximately \( 0.6667 \). This negative slope signifies that the line is decreasing.

Final Answer

The slope of the line is \(\boxed{-0.6667}\).

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