Question
Which of the following are ways to find the rate of change?
change in y over change in x
rise over run
subtract y coordinates over subtract x coordinates
all of the above
change in y over change in x
rise over run
subtract y coordinates over subtract x coordinates
all of the above
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GPT-4o mini
All of the options listed are ways to find the rate of change. They all describe the same concept mathematically:
1. **Change in y over change in x**: This is the most general definition of the rate of change, often represented mathematically as \(\frac{\Delta y}{\Delta x}\).
2. **Rise over run**: This phrase is commonly used in the context of a graph, where "rise" refers to the change in the y-coordinate and "run" refers to the change in the x-coordinate.
3. **Subtract y coordinates over subtract x coordinates**: This is essentially a more explicit way of expressing the same concept, where you calculate \(\frac{y_2 - y_1}{x_2 - x_1}\).
Since all these descriptions convey the same idea of the rate of change (slope of a line), the correct answer is **all of the above**.
1. **Change in y over change in x**: This is the most general definition of the rate of change, often represented mathematically as \(\frac{\Delta y}{\Delta x}\).
2. **Rise over run**: This phrase is commonly used in the context of a graph, where "rise" refers to the change in the y-coordinate and "run" refers to the change in the x-coordinate.
3. **Subtract y coordinates over subtract x coordinates**: This is essentially a more explicit way of expressing the same concept, where you calculate \(\frac{y_2 - y_1}{x_2 - x_1}\).
Since all these descriptions convey the same idea of the rate of change (slope of a line), the correct answer is **all of the above**.
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