To find the slope of the line that passes through the points \((-2, -19)\) and \((-12, 11)\), we use the slope formula. The slope \(m\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
In this case, we can assign the points as follows:
- \((x_1, y_1) = (-2, -19)\)
- \((x_2, y_2) = (-12, 11)\)
Now, we substitute the values into the slope formula:
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Identify the coordinates: \[ x_1 = -2, \quad y_1 = -19, \quad x_2 = -12, \quad y_2 = 11 \]
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Substitute into the formula: \[ m = \frac{11 - (-19)}{-12 - (-2)} \]
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Simplify the numerator: \[ 11 - (-19) = 11 + 19 = 30 \]
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Simplify the denominator: \[ -12 - (-2) = -12 + 2 = -10 \]
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Now we have: \[ m = \frac{30}{-10} \]
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Simplify the fraction: \[ m = -3 \]
Therefore, the slope of the line that passes through the points \((-2, -19)\) and \((-12, 11)\) is \(\boxed{-3}\).