Question

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

Answer 1

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 \(-\frac{5}{4}\).