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

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