To derive the equation of the line in slope-intercept form \(y = mx + b\) using the points (0, 2) and (1, -1), we follow these steps:
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Identify the points:
- The first point is \((0, 2)\), which gives us the y-intercept \(b\).
- The second point is \((1, -1)\).
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Calculate the slope \(m\): The formula for the slope \(m\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Plugging in our points \((0, 2)\) and \((1, -1)\): \[ m = \frac{-1 - 2}{1 - 0} = \frac{-3}{1} = -3 \]
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Write the equation: Now that we have the slope \(m = -3\) and the y-intercept \(b = 2\) (from the point (0, 2)), we can write the equation of the line in slope-intercept form: \[ y = -3x + 2 \]
Thus, the equation of the line is \(\boxed{y = -3x + 2}\).
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