To write the equation \( y - 2 = \frac{2}{5}(x + 2) \) in slope-intercept form, we need to solve for \( y \).
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Start with the original equation: \[ y - 2 = \frac{2}{5}(x + 2) \]
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Distribute \( \frac{2}{5} \) on the right side: \[ y - 2 = \frac{2}{5}x + \frac{2}{5} \cdot 2 \] \[ y - 2 = \frac{2}{5}x + \frac{4}{5} \]
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Now, add 2 to both sides to isolate \( y \): \[ y = \frac{2}{5}x + \frac{4}{5} + 2 \]
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Convert the 2 to a fraction with a denominator of 5: \[ 2 = \frac{10}{5} \]
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Add the fractions on the right side: \[ y = \frac{2}{5}x + \frac{4}{5} + \frac{10}{5} \] \[ y = \frac{2}{5}x + \frac{14}{5} \]
Thus, the equation in slope-intercept form \( y = mx + b \) is: \[ y = \frac{2}{5}x + \frac{14}{5} \]
Here, the slope \( m \) is \( \frac{2}{5} \) and the y-intercept \( b \) is \( \frac{14}{5} \).