Question

What is the slope of the line through
\[(1,-1)\] and
\[(5,-7)\]?
Choose 1 answer:
Choose 1 answer:
(Choice A)

\[\dfrac{3}2\]
A

\[\dfrac{3}2\]
(Choice B)

\[-\dfrac{2}3\]
B

\[-\dfrac{2}3\]
(Choice C)

\[-\dfrac{3}2\]
C

\[-\dfrac{3}2\]
(Choice D)

\[\dfrac{2}3\]
D

\[\dfrac{2}3\]

Answer 1

To find the slope of the line that passes through the points \((1, -1)\) and \((5, -7)\), we can use the formula for the slope \(m\):

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

Here, we can assign:
- \((x_1, y_1) = (1, -1)\)
- \((x_2, y_2) = (5, -7)\)

Now substitute these values into the slope formula:

\[
m = \frac{-7 - (-1)}{5 - 1}
\]

This simplifies to:

\[
m = \frac{-7 + 1}{5 - 1} = \frac{-6}{4}
\]

Now, simplify \(\frac{-6}{4}\):

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

Therefore, the slope of the line is

\[
\boxed{-\frac{3}{2}}
\]

This corresponds to Choice C.