Put the following equation of a line into slope-intercept form, simplifying all fractions.
2, x, plus, 6, y, equals, 36
2x+6y=
36

The given equation is:

\[
2x + 6y = 36
\]

To convert this into slope-intercept form (\(y = mx + b\)), we need to solve for \(y\).

### Step 1: Subtract \(2x\) from both sides:
\[
6y = -2x + 36
\]

### Step 2: Divide through by 6 to isolate \(y\):
\[
y = \frac{-2x + 36}{6}
\]

### Step 3: Simplify each term:
\[
y = \frac{-2x}{6} + \frac{36}{6}
\]

\[
y = -\frac{1}{3}x + 6
\]

So, the equation in slope-intercept form is:

\[
y = -\frac{1}{3}x + 6
\]

Would you like more details or have any questions?

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Here are 5 related questions to expand on this topic:
1. What is the slope of the line \(y = -\frac{1}{3}x + 6\)?
2. How do you find the y-intercept of a line?
3. What is the equation of a line parallel to \(y = -\frac{1}{3}x + 6\)?
4. How do you convert from slope-intercept form to standard form?
5. What does the slope represent in real-world problems?

**Tip:** When converting to slope-intercept form, always isolate \(y\) by performing inverse operations.

Put the following equation of a line into slope-intercept form, simplifying all fractions: 2x + 6y = 36

Learn how to convert the linear equation 2x + 6y = 36 into slope-intercept form (y = mx + b) with a step-by-step explanation. This problem involves key algebraic concepts and is suitable for students in Grades 8-10.

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