To find the slope and y-intercept of the equation \( 7x + 2y = 25 \) that has infinite solutions, we need to express the equation in the slope-intercept form, \( y = mx + b \), where \( m \) represents the slope and \( b \) represents the y-intercept.
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Start with the original equation: \[ 7x + 2y = 25 \]
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Isolate \( y \): \[ 2y = -7x + 25 \]
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Divide everything by 2 to solve for \( y \): \[ y = -\frac{7}{2}x + \frac{25}{2} \]
From the equation \( y = -\frac{7}{2}x + \frac{25}{2} \):
- The slope (\( m \)) is \( -\frac{7}{2} \).
- The y-intercept (\( b \)) is \( \frac{25}{2} \).
Thus, the final answer is:
The slope would be \( -\frac{7}{2} \).
The y-intercept would be \( \frac{25}{2} \).