What is the correct set up to finding the slope of a line that passes through the points (6, -3) and (-2, 7) ?

To find the slope of a line that passes through the points \((x_1, y_1)\) and \((x_2, y_2)\), you use the formula:

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

Given the points \((6, -3)\) and \((-2, 7)\), we can assign:

• \(x_1 = 6\), \(y_1 = -3\)
• \(x_2 = -2\), \(y_2 = 7\)

Plugging these values into the slope formula gives us:

\[ \text{slope} = \frac{7 - (-3)}{-2 - 6} \]

This simplifies to:

\[ \text{slope} = \frac{7 + 3}{-2 - 6} = \frac{10}{-8} = -\frac{5}{4} \]

Now, let's compare this to the answer choices:

• A. \(\frac{6 - (-3)}{-2 - 7}\) \(\Rightarrow \frac{6 + 3}{-9}\) (incorrect)
• B. \(\frac{6 - 2}{-3 + 7}\) \(\Rightarrow \frac{4}{4} = 1\) (incorrect)
• C. \(\frac{7 - 3}{-2 - 6}\) \(\Rightarrow \frac{4}{-8} = -\frac{1}{2}\) (incorrect)
• D. \(\frac{7 - (-3)}{-2 - 6}\) \(\Rightarrow \frac{7 + 3}{-8} = \frac{10}{-8} = -\frac{5}{4}\) (correct)

The correct set up is D: \(\frac{7 - (-3)}{-2 - 6}\).