To write the inequality [tex]\(6x - 2y > 12\)[/tex] in slope-intercept form, follow these steps:
1. Start with the given inequality:
[tex]\[
6x - 2y > 12
\][/tex]
2. Isolate the [tex]\(y\)[/tex]-term by moving [tex]\(6x\)[/tex] to the other side:
[tex]\[
-2y > -6x + 12
\][/tex]
3. Divide every term by [tex]\(-2\)[/tex] to solve for [tex]\(y\)[/tex]. Note that dividing by a negative number reverses the inequality sign:
[tex]\[
y < \frac{-6x}{-2} + \frac{12}{-2}
\][/tex]
4. Simplify the terms:
[tex]\[
y < 3x - 6
\][/tex]
So, the inequality written in slope-intercept form is:
[tex]\[
y < 3x - 6
\][/tex]
This matches the inequality given as an option, and hence the correct choice is:
[tex]\[
y < 3x - 6
\][/tex]
