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Transform the linear equation −2y=14−6x to slope-intercept form.

y= __

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To convert the equation \(-2y = 14 - 6x\) to slope-intercept form, which is \(y = mx + b\) (where \(m\) is the slope and \(b\) is the y-intercept), follow these steps:

  1. Start with the original equation:

    \[ -2y = 14 - 6x \]

  2. Divide every term by \(-2\) to solve for \(y\):

    \[ y = \frac{14}{-2} - \frac{6x}{-2} \]

  3. Simplifying the fractions gives:

    \[ y = -7 + 3x \]

  4. This can be rearranged to:

    \[ y = 3x - 7 \]

So the equation in slope-intercept form is:

\[ y = 3x - 7 \]