To find the slope of a line that passes through two points \((x_1, y_1)\) and \((x_2, y_2)\), you can use the slope formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
In this case, the points you have are \((6, -3)\) and \((-2, 7)\). We can assign:
- \((x_1, y_1) = (6, -3)\)
- \((x_2, y_2) = (-2, 7)\)
Now, let's plug the values into the slope formula:
\[ m = \frac{7 - (-3)}{-2 - 6} \]
Now simplify the expression:
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Calculate \(y_2 - y_1\): \[ 7 - (-3) = 7 + 3 = 10 \]
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Calculate \(x_2 - x_1\): \[ -2 - 6 = -8 \]
Now substitute these results back into the formula:
\[ m = \frac{10}{-8} = -\frac{5}{4} \]
Thus, the slope of the line that passes through the points \((6, -3)\) and \((-2, 7)\) is \(-\frac{5}{4}\).