To transform the linear equation \(-2y = 14 - 6x\) into slope-intercept form, we need to solve for \(y\) in terms of \(x\). The slope-intercept form of a linear equation is given by \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.
Starting with the equation:
\[ -2y = 14 - 6x \]
We want to isolate \(y\). First, divide both sides of the equation by \(-2\):
\[ y = \frac{14 - 6x}{-2} \]
Now, we can split the fraction:
\[ y = \frac{14}{-2} - \frac{6x}{-2} \]
This simplifies to:
\[ y = -7 + 3x \]
To put this in standard slope-intercept form \(y = mx + b\), we can rearrange it:
\[ y = 3x - 7 \]
Now, the equation in slope-intercept form is:
\[ y = 3x - 7 \]
In this equation, the slope \(m\) is \(3\) and the y-intercept \(b\) is \(-7\).