To find the formula that fits the points (1, 5), (2, 7), (3, 9), and (4, 11), we can start by observing the relationship between x and y in the given points.
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Calculate the slope (m): The change in y divided by the change in x gives us the slope.
From the points:
- For (1, 5) and (2, 7): \[ m = \frac{7 - 5}{2 - 1} = \frac{2}{1} = 2 \]
Similarly, from (2, 7) to (3, 9): \[ m = \frac{9 - 7}{3 - 2} = \frac{2}{1} = 2 \]
And from (3, 9) to (4, 11): \[ m = \frac{11 - 9}{4 - 3} = \frac{2}{1} = 2 \]
So, the slope \(m\) is consistently 2.
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Use the point-slope form of the linear equation: We can use one of the points, for example, (1, 5). The point-slope form of a line is given by: \[ y - y_1 = m(x - x_1) \]
Plugging in the values: \[ y - 5 = 2(x - 1) \]
Simplifying: \[ y - 5 = 2x - 2 \] \[ y = 2x + 3 \]
Thus, the final equation that represents the described points is: \[ \boxed{y = 2x + 3} \] Therefore, the correct option from the choices provided is y = 2x + 3.