To determine the slope of the line represented by the equation [tex]\(2x - 3y = 6\)[/tex], we need to convert it to the slope-intercept form, [tex]\(y = mx + b\)[/tex], where [tex]\(m\)[/tex] is the slope of the line.
Here are the steps to find the slope:
1. Start with the given equation:
[tex]\[
2x - 3y = 6
\][/tex]
2. Solve for [tex]\(y\)[/tex]:
- Isolate the [tex]\(y\)[/tex] term on one side of the equation:
[tex]\[
-3y = -2x + 6
\][/tex]
- Divide every term by [tex]\(-3\)[/tex]:
[tex]\[
y = \frac{2}{3}x - 2
\][/tex]
3. Identify the slope:
From the equation in slope-intercept form, [tex]\(y = mx + b\)[/tex], the coefficient of [tex]\(x\)[/tex] is the slope [tex]\(m\)[/tex]. Here, [tex]\(m = \frac{2}{3}\)[/tex].
Thus, the slope of the line represented by the equation [tex]\(2x - 3y = 6\)[/tex] is [tex]\(\frac{2}{3}\)[/tex].
Now, let's match this with the given choices:
a. [tex]\(-2 / 3\)[/tex]
b. [tex]\(2 / 3\)[/tex]
c. 3
d. [tex]\(-3 / 2\)[/tex]
The correct choice is:
b. [tex]\(2 / 3\)[/tex]
Therefore, the answer is:
[tex]\[ \boxed{2} \][/tex]
