what is the slope intercept for 2x+3y = 6

To find the slope-intercept form of the equation \(2x + 3y = 6\), we need to solve for \(y\) in terms of \(x\) and write the equation in the form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.

Here’s the step-by-step process:

1. Start with the equation:
   \[
   2x + 3y = 6
   \]

2. Subtract \(2x\) from both sides to isolate the \(y\) term:
   \[
   3y = -2x + 6
   \]

3. Divide both sides by 3 to solve for \(y\):
   \[
   y = -\frac{2}{3}x + 2
   \]

Now the equation is in slope-intercept form \(y = mx + b\), where:

- The slope (\(m\)) is \(-\frac{2}{3}\).
- The y-intercept (\(b\)) is \(2\).

### Do you want more details or have any questions?

Here are 5 related questions to expand your understanding:

1. How do you find the slope given two points on a line?
2. What is the significance of the y-intercept in a linear equation?
3. How would you convert a slope-intercept form equation back to standard form?
4. Can you graph the equation \(y = -\frac{2}{3}x + 2\)?
5. What is the effect on the graph if the slope is positive instead of negative?

**Tip:** When graphing a line, start by plotting the y-intercept and then use the slope to find another point on the line.

What is the slope intercept for 2x + 3y = 6?

Discover how to convert the linear equation 2x + 3y = 6 into slope-intercept form (y = mx + b) with a detailed, step-by-step guide. This problem focuses on key algebraic concepts such as slope and y-intercept, making it ideal for students in Grades 8-10.

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