Question
Find the slope of the line that goes through the given points. \( (9,-6) \) and \( (6,9) \) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The slope is \( \square \). (Type an integer or a simplified fraction.) B. The slope is undefined.
Ask by Todd Bates. in the United States
Mar 11,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The slope of the line is -5.
Solution
1. Identify the coordinates: Let \( (9,-6) \) be \((x_1, y_1)\) and \( (6,9) \) be \((x_2, y_2)\).
2. Use the slope formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
3. Substitute the values:
\[
m = \frac{9 - (-6)}{6 - 9}
\]
4. Simplify the numerator:
\[
9 - (-6) = 9 + 6 = 15
\]
5. Simplify the denominator:
\[
6 - 9 = -3
\]
6. Calculate the slope:
\[
m = \frac{15}{-3} = -5
\]
Thus, the slope of the line is \( \boxed{-5} \).
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Simplify this solution Mind Expander
To find the slope of a line that passes through two points, you can use the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Using the points \( (9, -6) \) and \( (6, 9) \), let's label them: - \( (x_1, y_1) = (9, -6) \) - \( (x_2, y_2) = (6, 9) \) Now, plug the values into the formula: \[ m = \frac{9 - (-6)}{6 - 9} = \frac{9 + 6}{6 - 9} = \frac{15}{-3} = -5 \] So the slope is \( -5 \). Thus, the correct choice is: A. The slope is \( -5 \).
