To transform the linear equation \( 4x - 8y = 24 \) into slope-intercept form, which is given by \( y = mx + b \) (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 term containing \( y \) by moving \( 4x \) to the other side of the equation: \[ -8y = -4x + 24 \]
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Divide every term by \(-8\) to solve for \( y \): \[ y = \frac{-4}{-8}x + \frac{24}{-8} \]
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Simplify the fractions: \[ y = \frac{1}{2}x - 3 \]
Thus, the equation in slope-intercept form is: \[ y = \frac{1}{2}x - 3 \]
Here, the slope \( m \) is \( \frac{1}{2} \) and the y-intercept \( b \) is \(-3\).
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