To find the slope of the linear function given by the equation \(10x + 2y = 6\), we can rearrange it into the slope-intercept form, which is \(y = mx + b\), where \(m\) represents the slope.
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Start with the equation: \[ 10x + 2y = 6 \]
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Solve for \(y\):
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First, isolate \(2y\) by subtracting \(10x\) from both sides: \[ 2y = -10x + 6 \]
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Next, divide every term by \(2\) to solve for \(y\): \[ y = -5x + 3 \]
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Now, the equation is in slope-intercept form \(y = mx + b\), where \(m\) is the slope.
From the equation \(y = -5x + 3\), we can see that the slope \(m\) is: \[ m = -5 \]
Thus, the slope of the function is \(\boxed{-5}\).