To determine the slope of the line given by the equation [tex]\(4x + 2y = 12\)[/tex], we need to convert this equation into its slope-intercept form, which is [tex]\(y = mx + b\)[/tex], where [tex]\(m\)[/tex] represents the slope of the line.
Here are the steps to do that:
1. Start with the given equation:
[tex]\[ 4x + 2y = 12 \][/tex]
2. Isolate the [tex]\(y\)[/tex] term by first subtracting [tex]\(4x\)[/tex] from both sides of the equation:
[tex]\[ 2y = -4x + 12 \][/tex]
3. Next, solve for [tex]\(y\)[/tex] by dividing every term in the equation by 2:
[tex]\[ y = -2x + 6 \][/tex]
In the equation [tex]\(y = -2x + 6\)[/tex], the coefficient of [tex]\(x\)[/tex] is the slope [tex]\(m\)[/tex].
Therefore, the slope of the line is:
[tex]\[ \boxed{-2} \][/tex]
So the correct answer is:
C. -2
