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 \(m\) is the slope and \(b\) is the y-intercept.
Here are the steps to do that:
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Start with the original equation: \[ 10x + 2y = 6 \]
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Solve for \(y\) by isolating it on one side of the equation. First, subtract \(10x\) from both sides: \[ 2y = -10x + 6 \]
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Now, divide every term by 2 to solve for \(y\): \[ y = -5x + 3 \]
Now the equation is in the slope-intercept form \(y = mx + b\), where:
- The slope \(m\) is \(-5\).
- The y-intercept \(b\) is \(3\).
Therefore, the slope \(m\) of the linear function is: \[ \boxed{-5} \]