To determine the slope of the line represented by the equation [tex]\(12x - 4y = 3\)[/tex], we need to rewrite this equation in the slope-intercept form, which is [tex]\(y = mx + b\)[/tex], where [tex]\(m\)[/tex] represents the slope.
1. Starting with the given equation:
[tex]\[
12x - 4y = 3
\][/tex]
2. Isolate the term involving [tex]\(y\)[/tex]. To do this, subtract [tex]\(12x\)[/tex] from both sides of the equation:
[tex]\[
-4y = -12x + 3
\][/tex]
3. Next, we need to solve for [tex]\(y\)[/tex]. To do this, divide every term in the equation by [tex]\(-4\)[/tex]:
[tex]\[
y = \frac{-12}{-4}x + \frac{3}{-4}
\][/tex]
4. Simplify the fractions:
[tex]\[
y = 3x - \frac{3}{4}
\][/tex]
Now the equation is in the slope-intercept form [tex]\(y = mx + b\)[/tex], where the slope [tex]\(m\)[/tex] is the coefficient of [tex]\(x\)[/tex].
Therefore, the slope of Helaine's line is:
[tex]\[
m = 3
\][/tex]
Thus, the correct answer is:
[tex]\[
3
\][/tex]
