Select the correct answer.

What is the slope of the line represented by this equation?

-3x + 8y = 12

A. -[tex]\(\frac{8}{3}\)[/tex]

B. -[tex]\(\frac{3}{8}\)[/tex]

C. [tex]\(\frac{3}{8}\)[/tex]

D. [tex]\(\frac{8}{3}\)[/tex]



Answer :

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]