To write the equation of the line in slope-intercept form (y = mx + b), we need to determine the slope (m) and the y-intercept (b).
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Identify the points:
- The line passes through the points (0, 2) and (1, -1).
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Calculate the slope (m): The slope formula is: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Using the points (0, 2) and (1, -1): \[ m = \frac{-1 - 2}{1 - 0} = \frac{-3}{1} = -3 \]
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Identify the y-intercept (b): The y-intercept is the value of y when x = 0. From the point (0, 2), we see that: \[ b = 2 \]
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Write the equation: Now that we have the slope and the y-intercept, we can write the equation of the line: \[ y = -3x + 2 \]
Thus, the equation in slope-intercept form for the line is: \[ \boxed{y = -3x + 2} \]
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