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To find the slope of a line containing the pair of points \((-5, 7)\) and \((6, -4)\), we use the slope formula:

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

where \((x_1, y_1) = (-5, 7)\) and \((x_2, y_2) = (6, -4)\).

Substitute the values into the formula:

\[
m = \frac{-4 - 7}{6 - (-5)} = \frac{-4 - 7}{6 + 5} = \frac{-11}{11} = -1
\]

So, the slope is \(-1\).

Answer choice A is correct: "The slope is \(-1\)."

Do you want more details, or have any further questions?

Here are 5 related questions to expand your understanding:
1. What happens if both points have the same \(x\)-coordinate? How would the slope be defined then?
2. How would you find the slope of a line if given an equation like \(y = 2x + 3\)?
3. Can you calculate the slope of a vertical line? Why or why not?
4. How would the slope change if you switch the points' order in the formula?
5. How can the slope help determine whether two lines are parallel or perpendicular?

**Tip:** Remember, if two lines have the same slope, they are parallel. If their slopes are negative reciprocals, they are perpendicular!

Find the slope of the line containing the pair of points (-5, 7) and (6, -4).

Learn how to calculate the slope of a line given two points: (-5, 7) and (6, -4). This problem applies the slope formula and is suitable for students in Grades 8-10.

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