Question

What is the slope of the line that contains the points negative 3, negative five halves and (3, −8)?

negative eleven fourths
negative eleven twelfths
eleven fourths
eleven twelfths

Answer 1

To find the slope of the line that contains the points \((-3, -\frac{5}{2})\) and \((3, -8)\), we can use the formula for the slope \( m \):

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

Where:
- \((x_1, y_1) = (-3, -\frac{5}{2})\)
- \((x_2, y_2) = (3, -8)\)

Now, let's calculate the slope:

1. **Identify the coordinates**:
- \(x_1 = -3\)
- \(y_1 = -\frac{5}{2}\)
- \(x_2 = 3\)
- \(y_2 = -8\)

2. **Substitute into the slope formula**:
\[
m = \frac{-8 - (-\frac{5}{2})}{3 - (-3)}
\]

3. **Simplify the numerator**:
\[
-8 + \frac{5}{2} = -\frac{16}{2} + \frac{5}{2} = -\frac{16 - 5}{2} = -\frac{11}{2}
\]

4. **Calculate the denominator**:
\[
3 - (-3) = 3 + 3 = 6
\]

5. **Combine the results**:
\[
m = \frac{-\frac{11}{2}}{6}
\]

6. **Divide by 6**:
\[
m = -\frac{11}{2} \times \frac{1}{6} = -\frac{11}{12}
\]

Therefore, the slope of the line is:

\[
\boxed{-\frac{11}{12}}
\]

This corresponds to the option negative eleven twelfths.