To determine the slope of the line passing through the points (7, 10) and (7, 20), we can use the slope formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
In this case, let's assign:
- Point 1: \( (x_1, y_1) = (7, 10) \)
- Point 2: \( (x_2, y_2) = (7, 20) \)
Now, substituting the values into the slope formula:
\[ m = \frac{20 - 10}{7 - 7} = \frac{10}{0} \]
Since the denominator is zero, the slope \( m \) is undefined. This means that the line is vertical.
Now, let's analyze the statements:
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"It has a slope of zero because x 2 minus x 1... is zero..." - This is incorrect. The slope is not zero; it is undefined.
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"It has a slope of zero because x 2 minus x 1... is zero, and the denominator of a fraction cannot be zero." - This is also incorrect. Again, the slope is undefined, not zero.
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"It has no slope because x 2 minus x 1... is zero, and the numerator of a fraction cannot be zero." - This statement is misleading; while it is correct that the denominator is zero, it wrongly says the reason relates to the numerator.
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"It has no slope because x 2 minus x 1... is zero, and the denominator of a fraction cannot be zero." - This is the most accurate statement. Since \( x_1 = x_2 = 7 \), the denominator is zero, which means the line is vertical and thus has no defined slope.
Therefore, the correct statement about the line is the fourth option: It has no slope because \( x_2 - x_1 \) in the formula is zero, and the denominator of a fraction cannot be zero.
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