To transform the linear equation \( 4x - 8y = 24 \) into slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept, follow these steps:
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Start with the original equation: \[ 4x - 8y = 24 \]
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Isolate the \( y \) term: \[ -8y = -4x + 24 \]
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Divide each term by \(-8\) to solve for \( y \): \[ y = \frac{-4}{-8}x + \frac{24}{-8} \]
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Simplify the fractions: \[ y = \frac{1}{2}x - 3 \]
So, the equation in slope-intercept form is: \[ y = \frac{1}{2}x - 3 \]
None of the provided responses match this simplified form exactly, but if the intention was to check for the equivalent intermediate transformation (before simplification), the correct response based on the choices given would be: \[ −8y=−4x+24 \]