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

To put the equation of the line \(2x + 6y = 36\) into slope-intercept form, \(y = mx + b\), we need to solve for \(y\).

### Steps:
1. Start with the equation:
   \[
   2x + 6y = 36
   \]
2. Subtract \(2x\) from both sides to isolate the \(y\)-term:
   \[
   6y = -2x + 36
   \]
3. Divide every term by 6 to solve for \(y\):
   \[
   y = \frac{-2x}{6} + \frac{36}{6}
   \]
4. Simplify the fractions:
   \[
   y = \frac{-x}{3} + 6
   \]

So, the equation in slope-intercept form is:
\[
y = -\frac{1}{3}x + 6
\]

The slope \(m\) is \(-\frac{1}{3}\), and the y-intercept \(b\) is \(6\).

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Would you like more details on any part of the process? Here are five related questions to explore this concept further:

1. How do you determine the slope of a line from its equation?
2. What is the significance of the y-intercept in a graph?
3. How do you convert a slope-intercept equation back to standard form?
4. How do you graph a line using the slope and y-intercept?
5. Can you find the x-intercept of this line?

**Tip:** When dividing each term of an equation by a constant, make sure to apply the division to both sides and simplify the fractions carefully.

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). Follow step-by-step instructions to simplify fractions and find the slope and y-intercept. Ideal for students in Grades 8-10.

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