Question

What is the slope of the line that passes through the points left parenthesis, 9, comma, minus, 5, right parenthesis(9,−5) and left parenthesis, 1, comma, minus, 1, right parenthesis(1,−1)? Write your answer in simplest form.

Answer 1

To find the slope of the line that passes through the points \((9, -5)\) and \((1, -1)\), we can use the formula for the slope \(m\):

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

Here, we need to identify the coordinates of the points:
- Let \((x_1, y_1) = (9, -5)\)
- Let \((x_2, y_2) = (1, -1)\)

Now, substituting the coordinates into the slope formula:

\[
m = \frac{-1 - (-5)}{1 - 9}
\]

Calculating the numerator:

\[
-1 - (-5) = -1 + 5 = 4
\]

Calculating the denominator:

\[
1 - 9 = -8
\]

Now substituting these values back into the slope formula:

\[
m = \frac{4}{-8} = -\frac{1}{2}
\]

Thus, the slope of the line that passes through the points \((9, -5)\) and \((1, -1)\) is

\[
\boxed{-\frac{1}{2}}
\]