Answered

Welcome to Westonci.ca, where curiosity meets expertise. Ask any question and receive fast, accurate answers from our knowledgeable community. Discover comprehensive answers to your questions from knowledgeable professionals on our user-friendly platform. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.

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]
Thanks for using our service. We aim to provide the most accurate answers for all your queries. Visit us again for more insights. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.