Question
Find the slope of the line passing through the pair of points or state that the slope is undefined. Then indicate whether the line through the points rises, falls, is horizontal, or is vertical. \( (2,7) \) and \( (-6,-9) \) Select the correct choice below and fill in the answer box within your choice. A. The slope is \( \square \). (Simplify your answer.) B. The slope is undefined.
Ask by Wilson Parry. in the United States
Mar 12,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
A. The slope is 2. The line rises.
Solution
To find the slope of the line passing through the points \( (2,7) \) and \( (-6,-9) \), we can use the slope formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
where \( (x_1, y_1) = (2, 7) \) and \( (x_2, y_2) = (-6, -9) \).
Now, let's substitute the values into the formula:
1. Calculate \( y_2 - y_1 \):
\[
y_2 - y_1 = -9 - 7 = -16
\]
2. Calculate \( x_2 - x_1 \):
\[
x_2 - x_1 = -6 - 2 = -8
\]
3. Now, substitute these results into the slope formula:
\[
m = \frac{-16}{-8}
\]
4. Simplify the fraction:
\[
m = 2
\]
Now that we have the slope, we can determine the behavior of the line:
- Since the slope \( m = 2 \) is positive, the line rises.
Thus, the correct choice is:
A. The slope is \( 2 \). (Simplify your answer.)
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Simplify this solution Bonus Knowledge
To find the slope of the line passing through the points \((2, 7)\) and \((-6, -9)\), we use the formula for slope: \[ \text{slope} (m) = \frac{y_2 - y_1}{x_2 - x_1} \] Substituting the coordinates of the points: \[ m = \frac{-9 - 7}{-6 - 2} = \frac{-16}{-8} = 2 \] A. The slope is \(2\). The line rises as it moves from left to right. The line rises because the slope is positive, indicating that as we move along the x-axis in the positive direction, the line moves upward in the y-axis direction. This is a classic characteristic of lines with positive slopes!
