Question

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

1. Calculate \(y_2 - y_1\):
\[
7 - (-3) = 7 + 3 = 10
\]

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