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 your case, the points are \((6, -3)\) and \((-2, 7)\). Assign the coordinates as follows:
- \( (x_1, y_1) = (6, -3) \)
- \( (x_2, y_2) = (-2, 7) \)
Now, plug these values into the slope formula:
\[ m = \frac{7 - (-3)}{-2 - 6} \]
This simplifies to:
\[ m = \frac{7 + 3}{-2 - 6} \]
\[ m = \frac{10}{-8} \]
\[ m = -\frac{5}{4} \]
Thus, the slope of the line passing through the points \((6, -3)\) and \((-2, 7)\) is \(-\frac{5}{4}\).