To determine whether a value represents the slope of the line defined by points A (0, 2.5) and B (0.833, 0), we need to calculate the slope using the formula:
\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \]
Here, \( (x_1, y_1) = (0, 2.5) \) and \( (x_2, y_2) = (0.833, 0) \). Plugging the coordinates into the formula:
\[ \text{slope} = \frac{0 - 2.5}{0.833 - 0} = \frac{-2.5}{0.833} \]
Calculating that value gives a negative result, confirming that the slope of the line is indeed negative.
Now let's go through the statements provided:
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The y-intercept is not - (missing value): This statement is only about the y-intercept and does not directly pertain to the slope.
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The line slants downward, so the slope is negative: This statement is true and confirms that the slope is negative.
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A slope cannot be a mixed number: This statement is incorrect; slopes can indeed be expressed as mixed numbers.
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The change in y from A to B is negative: This is a factual statement about the points, indicating that the line decreases from A to B, which is consistent with a negative slope.
A clear and simple way to conclude that a given value is not the slope of this graph is the statement "The line slants downward, so the slope is negative," if the slope provided is positive (or zero), indicating that it does not match the actual slope calculated from points A and B. If the indicated slope value is positive or zero, it's not correct.