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Write the inequality in slope-intercept form:

[tex]\[ 6x - 2y \ \textgreater \ 12 \][/tex]

A. [tex]\( y \ \textgreater \ -6 + 3x \)[/tex]

B. [tex]\( y \ \textgreater \ -6 - 3x \)[/tex]

C. [tex]\( y \ \textless \ -6 + 3x \)[/tex]

D. [tex]\( y \ \textless \ -6 - 3x \)[/tex]

Sagot :

GinnyAnswer
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]
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