Answer: The slope of a line parallel to 4x - 2y = -12 is <em>(m=6),</em> or just <em>6</em>.
Step-by-step explanation:
In order to find the slope of the equation, we must first change the equation from standard form into slope-intercept form.
First things first is to subtract 4x from both side so that the <em>y</em> and slope are not on the same side of the equation, and so that the slope and y-intercept are on the same side of the equation.
4x - 2y = -12
<u>-4x</u> <u>-4x</u>
-2y = -4x - 12
Subtracting 4x from both sides of the equation successfully transforms the equation from standard form into slope-intercept form and gives you the equation <em>-2y = -4x - 12.</em>
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The next step is to make sure that the <em>y </em>is positive. It is also necessary to ensure that there is no coefficient. The way to do that is to divide all terms on both sides of the equation by <em>-2</em>.
<u>-2y = -4x - 12</u>
-2
y = 4x + 6
Dividing both sides of the equation by -2 correctly and fully transforms the equation into the slope-intercept form and as well gives us the equation <em>y = 4x + 6.</em> From this equation we can see that the slope of the equation is 6, or <em>(m=6)</em>.
Since the slopes of all parallel lines are exactly the same, we can conclude that the slope of a line parallel to 4x - 2y = -12 <em>(y = 4x + 6)</em> is 6.
