To find the equation of the line connecting the points (0, 2) and (8, 10), we can use the formula for the slope \( m \) and the equation of a line.
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Calculate the slope \( m \): \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{10 - 2}{8 - 0} = \frac{8}{8} = 1 \]
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Use the point-slope form of the equation of a line: \[ y - y_1 = m(x - x_1) \] We can use point (0, 2) as \( (x_1, y_1) \): \[ y - 2 = 1(x - 0) \quad \Rightarrow \quad y - 2 = x \] Rearranging this gives: \[ y = x + 2 \]
So the equation of the line from (0, 2) to (8, 10) is: \[ y = x + 2 \]
Next, let's verify if the other points (2, 4), (5, 7), and (7, 8) are on the line:
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For (2, 4): \[ y = 2 + 2 = 4 \quad \text{(point lies on the line)} \]
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For (5, 7): \[ y = 5 + 2 = 7 \quad \text{(point lies on the line)} \]
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For (7, 8): \[ y = 7 + 2 = 9 \quad \text{(this point does not lie on the line, since we get 9 instead of 8)} \]
In summary:
- The equation of the line connecting (0, 2) and (8, 10) is \( y = x + 2 \).
- The points (2, 4) and (5, 7) lie on the line, while (7, 8) does not.