https://file.aiquickdraw.com/mathbot/file/172661647491748d1637a.jpg

The question asks for the equation \( 2x + 6y = -12 \) to be solved for \( y \).

Let's solve the equation step by step:

### Step 1: Isolate the \( y \)-term
We start by moving the \( 2x \) to the other side of the equation:
\[
6y = -12 - 2x
\]
which can be rewritten as:
\[
6y = -2x - 12
\]

### Step 2: Solve for \( y \)
Now, divide both sides of the equation by 6 to isolate \( y \):
\[
y = \frac{-2x - 12}{6}
\]
Simplifying the right-hand side:
\[
y = \frac{-2x}{6} + \frac{-12}{6}
\]
\[
y = \frac{-1}{3}x - 2
\]

This matches option **b: \( y = -\frac{1}{3}x - 2 \)**.

Would you like more details or have any questions?

Here are 5 related questions to expand on this:
1. How do you graph the equation \( y = -\frac{1}{3}x - 2 \)?
2. What does the slope \( -\frac{1}{3} \) indicate about the graph's steepness?
3. Can you rearrange other linear equations to slope-intercept form?
4. What is the y-intercept of \( y = -\frac{1}{3}x - 2 \), and how do you interpret it?
5. How would the equation change if the slope were positive?

**Tip:** When solving linear equations, aim to isolate the variable step by step, and always simplify fractions for clarity.

Which of the following shows the equation solved for y? 2x + 6y = -12

Learn how to solve the linear equation 2x + 6y = -12 for y, step-by-step. This problem involves algebraic manipulation to isolate y and express the equation in slope-intercept form. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation