To find the slope of the line represented by the equation [tex]\(-3x + 8y = 12\)[/tex], we need to rearrange it into slope-intercept form, which is [tex]\(y = mx + b\)[/tex], where [tex]\(m\)[/tex] is the slope.
Here is the step-by-step transformation:
1. Start with the given equation:
[tex]\[
-3x + 8y = 12
\][/tex]
2. Isolate the [tex]\(y\)[/tex]-term on one side of the equation. To do this, first add [tex]\(3x\)[/tex] to both sides of the equation:
[tex]\[
8y = 3x + 12
\][/tex]
3. Solve for [tex]\(y\)[/tex] by dividing every term on both sides of the equation by 8:
[tex]\[
y = \frac{3}{8}x + \frac{12}{8}
\][/tex]
4. Simplify the constant term on the right-hand side:
[tex]\[
y = \frac{3}{8}x + \frac{3}{2}
\][/tex]
In the equation [tex]\(y = \frac{3}{8}x + \frac{3}{2}\)[/tex], the coefficient of [tex]\(x\)[/tex] is the slope [tex]\(m\)[/tex]. Therefore, the slope of the line is:
[tex]\[
m = \frac{3}{8}
\][/tex]
Thus, the correct answer is:
C. [tex]\(\frac{3}{8}\)[/tex]
