Beck Dawson
08/13/2024 · Senior High School
Find the slope of the line passing through the points \( (6,6) \) and \( (6,-4) \). slope: \( \square \) Find the slope of the line passing through the points \( (-5,-6) \) and \( (-5,6) \)
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Step-by-step Solution
To find the slope of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\), we use the formula:
\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}
\]
1. For the points \((6, 6)\) and \((6, -4)\):
Here, \(x_1 = 6\), \(y_1 = 6\), \(x_2 = 6\), and \(y_2 = -4\).
Plugging in the values:
\[
\text{slope} = \frac{-4 - 6}{6 - 6} = \frac{-10}{0}
\]
Since the denominator is zero, the slope is undefined. This indicates that the line is vertical.
**Slope: undefined**
2. For the points \((-5, -6)\) and \((-5, 6)\):
Here, \(x_1 = -5\), \(y_1 = -6\), \(x_2 = -5\), and \(y_2 = 6\).
Plugging in the values:
\[
\text{slope} = \frac{6 - (-6)}{-5 - (-5)} = \frac{6 + 6}{-5 + 5} = \frac{12}{0}
\]
Again, since the denominator is zero, the slope is undefined. This also indicates that the line is vertical.
**Slope: undefined**
Quick Answer
The slope of the line passing through the points \( (6,6) \) and \( (6,-4) \) is undefined. The slope of the line passing through the points \( (-5,-6) \) and \( (-5,6) \) is also undefined.
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