To transform the linear equation \(4x - 8y = 24\) into slope-intercept form, which is \(y = mx + b\) (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 by subtracting \(4x\) from both sides: \[ -8y = -4x + 24 \]
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Next, divide every term by \(-8\) to solve for \(y\): \[ y = \frac{-4}{-8}x + \frac{24}{-8} \]
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Simplify the fractions: \[ y = \frac{1}{2}x - 3 \]
Now, the equation is in slope-intercept form:
\[ y = \frac{1}{2}x - 3 \]
Here, the slope \(m\) is \(\frac{1}{2}\) and the y-intercept \(b\) is \(-3\).
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