To find the slope and y-intercept of the equation \(8x + 2y = 25\) that has infinite solutions, we first need to express the equation in slope-intercept form, which is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.
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Start with the original equation: \[ 8x + 2y = 25 \]
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Isolate \(y\) on one side. First, subtract \(8x\) from both sides: \[ 2y = -8x + 25 \]
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Now divide every term by \(2\) to solve for \(y\): \[ y = -4x + 12.5 \]
From this form, we can identify the slope and the y-intercept:
- The slope (\(m\)) is \(-4\).
- The y-intercept (\(b\)) is \(12.5\).
Thus:
- The slope would be \(-4\).
- The y-intercept would be \(12.5\).
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