To convert the equation \(3x + 2y = 14\) to 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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Isolate the \(y\) term: \[ 2y = 14 - 3x \]
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Divide every term by 2 to solve for \(y\): \[ y = \frac{14}{2} - \frac{3}{2}x \] \[ y = 7 - \frac{3}{2}x \]
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Rewrite the equation: To match the standard slope-intercept form \(y = mx + b\), you can rearrange it: \[ y = -\frac{3}{2}x + 7 \]
Now the equation is in slope-intercept form, where the slope \(m = -\frac{3}{2}\) and the y-intercept \(b = 7\).