Question

What is the slope of the line containing (-3, 5) and (6, -1)?

Answer 1

To find the slope of the line that contains the points \((-3, 5)\) and \((6, -1)\), we can use the slope formula:

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

Here, let's assign the coordinates of the points:
- \((x_1, y_1) = (-3, 5)\)
- \((x_2, y_2) = (6, -1)\)

Now we can substitute these values into the formula:

\[
m = \frac{-1 - 5}{6 - (-3)}
\]

Calculating the numerator:

\[
-1 - 5 = -6
\]

Calculating the denominator:

\[
6 - (-3) = 6 + 3 = 9
\]

Now, substituting back into the formula gives us:

\[
m = \frac{-6}{9}
\]

This simplifies to:

\[
m = \frac{-2}{3}
\]

Thus, the slope of the line containing the points \((-3, 5)\) and \((6, -1)\) is \(\boxed{-\frac{2}{3}}\).