To find the equation of the line in slope-intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept, we can follow these steps:
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Calculate the slope (m): The slope \(m\) is given by the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Using the points \((-2, 2)\) and \((0, 1)\):
\[ m = \frac{1 - 2}{0 - (-2)} = \frac{-1}{2} = -\frac{1}{2} \]
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Substitute the slope and one of the points into the point-slope form to find b: We'll use the point \((0, 1)\), which is also the y-intercept.
Since the coordinates of this point are \(x = 0\) and \(y = 1\), we can directly see that \(b = 1\).
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Write the equation in slope-intercept form: Now that we have the slope and the y-intercept, we can write the equation of the line:
\[ y = -\frac{1}{2}x + 1 \]
Thus, the equation of the line in slope-intercept form is:
\[ y = -\frac{1}{2}x + 1 \]
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