What is the slope of the line represented by the equation [tex]2x - 3y = 6[/tex]?

Select one:
a. [tex]-\frac{2}{3}[/tex]
b. [tex]\frac{2}{3}[/tex]
c. 3
d. [tex]-\frac{3}{2}[/tex]



Answer :

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]