Question

What is the slope of the line that contains the points negative 2, negative seven halves and (4, −4)?
negative one twelfth
negative one fourth
one fourth
one twelfth

Answer 1

To find the slope of the line that contains the points \((-2, -\frac{7}{2})\) and \((4, -4)\), we can use the slope formula:

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

Here, let \((x_1, y_1) = (-2, -\frac{7}{2})\) and \((x_2, y_2) = (4, -4)\).

Substituting the coordinates into the slope formula:

\[
m = \frac{-4 - (-\frac{7}{2})}{4 - (-2)}
\]

Simplifying the numerator:

\[
-4 + \frac{7}{2} = -\frac{8}{2} + \frac{7}{2} = -\frac{1}{2}
\]

And the denominator:

\[
4 + 2 = 6
\]

Now substituting these into the slope formula:

\[
m = \frac{-\frac{1}{2}}{6}
\]

This can be simplified:

\[
m = -\frac{1}{2} \cdot \frac{1}{6} = -\frac{1}{12}
\]

Therefore, the slope of the line that contains the points \((-2, -\frac{7}{2})\) and \((4, -4)\) is:

\[
\boxed{-\frac{1}{12}}
\]