To rewrite the equation \( 4x + 3y = -9 \) in 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: \[ 4x + 3y = -9 \]
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Isolate \( y \) by moving \( 4x \) to the other side: \[ 3y = -4x - 9 \]
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Next, divide every term by \( 3 \) to solve for \( y \): \[ y = -\frac{4}{3}x - 3 \]
Now, the equation \( y = -\frac{4}{3}x - 3 \) is in slope-intercept form. Thus, the equivalent equation rewritten in slope-intercept form is: \[ y = -\frac{4}{3}x - 3 \]