Question
The park rangers at Blue Creek Park track the number of Chinook salmon that pass by a motion detector during migration season. This scatter plot shows some of their data along with the line of best fit.
The equation for the line of best fit is y=
2
5
x+7. According to the equation, which of these statements is true?
The equation for the line of best fit is y=
2
5
x+7. According to the equation, which of these statements is true?
Answers
GPT-4o mini
The equation for the line of best fit is given as \( y = \frac{2}{5}x + 7 \).
From this equation, we can interpret the slope and y-intercept. Here's what each part means:
1. **Slope (\(\frac{2}{5}\))**: For every increase of 1 in \(x\) (in this context, for every additional unit of whatever \(x\) represents, which could be time or a factor related to the salmon's migration), the value of \(y\) (the number of Chinook salmon detected) increases by \(\frac{2}{5}\). This indicates a positive correlation between the two variables; as \(x\) increases, the number of salmon detected tends to increase.
2. **Y-intercept (7)**: When \(x = 0\), \(y\) equals 7. This means that when the independent variable (whatever \(x\) represents) is zero, the model predicts that there will be approximately 7 Chinook salmon passing by the motion detector.
Now, based on this equation, the true statements could include:
- If more time passes (if \(x\) increases), the estimated salmon count \(y\) will also increase, indicating growth in the number of salmon passing.
- At \(x = 0\), the initial expected count of Chinook salmon is 7.
- The relationship between \(x\) and \(y\) is positive but moderate due to the slope of \( \frac{2}{5} \).
If you have specific statements you would like evaluated for their truthfulness based on this information, please list them.
From this equation, we can interpret the slope and y-intercept. Here's what each part means:
1. **Slope (\(\frac{2}{5}\))**: For every increase of 1 in \(x\) (in this context, for every additional unit of whatever \(x\) represents, which could be time or a factor related to the salmon's migration), the value of \(y\) (the number of Chinook salmon detected) increases by \(\frac{2}{5}\). This indicates a positive correlation between the two variables; as \(x\) increases, the number of salmon detected tends to increase.
2. **Y-intercept (7)**: When \(x = 0\), \(y\) equals 7. This means that when the independent variable (whatever \(x\) represents) is zero, the model predicts that there will be approximately 7 Chinook salmon passing by the motion detector.
Now, based on this equation, the true statements could include:
- If more time passes (if \(x\) increases), the estimated salmon count \(y\) will also increase, indicating growth in the number of salmon passing.
- At \(x = 0\), the initial expected count of Chinook salmon is 7.
- The relationship between \(x\) and \(y\) is positive but moderate due to the slope of \( \frac{2}{5} \).
If you have specific statements you would like evaluated for their truthfulness based on this information, please list them.