To provide you with a thoroughly answer, I'll need to make some assumptions since I don’t have access to specific data from "number 3."
Let’s assume you have a trend line from a scatter plot with several data points. Here's how you can compute the y-intercept, slope, and write the equation in the form \(y = mx + b\):
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Extend the trend line to cross the y-axis: To find the y-intercept, you'll look at where the trend line crosses the y-axis. This typically happens when \(x = 0\). The value of \(y\) at this point is the y-intercept (b).
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Determine the ordered pairs of two points: Assume that two points on your trend line are:
- Point 1: \( (x_1, y_1) \)
- Point 2: \( (x_2, y_2) \)
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Calculate the slope (m): The slope is calculated using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
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Write the equation in \(y = mx + b\) form: Once you have the slope (m) and the y-intercept (b), you can write the equation.
Example
Let’s assume:
- Points are \( (2, 3) \) and \( (4, 7) \)
- Y-intercept is \( 1 \)
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Calculate the slope: \[ m = \frac{7 - 3}{4 - 2} = \frac{4}{2} = 2 \]
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Write the equation: \[ y = 2x + 1 \]
Final Answer
The equation of the trend line is: \[ \boxed{y = 2x + 1} \]
Please replace the example with actual data points and y-intercept as per your specific case.