To determine which equations could represent Relationship B, we need to understand that Relationship B has a greater rate (slope) than Relationship A. From the description of Relationship A, we can deduce some information about its slope.
The points mentioned in Relationship A are (4, 2) and (8, 4). To find the slope (rate) of Relationship A, we can calculate the slope using the formula:
\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \]
Using the points (4, 2) and (8, 4) as \((x_1, y_1)\) and \((x_2, y_2)\):
\[ \text{slope} = \frac{4 - 2}{8 - 4} = \frac{2}{4} = \frac{1}{2} \]
So, the slope of Relationship A is \( \frac{1}{2} \).
Now, since Relationship B has a greater rate, we are looking for equations with a slope greater than \( \frac{1}{2} \).
Now let's evaluate the provided responses:
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\(y = 34x\): The slope is 34, which is greater than \( \frac{1}{2} \). (Valid)
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\(y = \frac{3}{4} x\): The slope is \( \frac{3}{4} \), which is greater than \( \frac{1}{2} \). (Valid)
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\(y = 14x\): The slope is 14, which is greater than \( \frac{1}{2} \). (Valid)
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\(y = \frac{1}{4} x\): The slope is \( \frac{1}{4} \), which is less than \( \frac{1}{2} \). (Not valid)
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\(y = \frac{2}{3} x\): The slope is \( \frac{2}{3} \), which is greater than \( \frac{1}{2} \). (Valid)
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\(y = 0.6 x\): The slope is 0.6, which is greater than \( \frac{1}{2} \). (Valid)
In summary, the equations that could represent Relationship B, having a greater rate than Relationship A, are:
- \(y = 34x\)
- \(y = \frac{3}{4} x\)
- \(y = 14x\)
- \(y = \frac{2}{3} x\)
- \(y = 0.6x\)
49 answers