convert 2x+3y=5 from standard for into slope-intercept form

To convert the equation \(2x + 3y = 5\) from standard form (Ax + By = C) into slope-intercept form (y = mx + b), we need to solve for \(y\).

### Steps to Convert:

1. **Start with the given equation:**
   \[
   2x + 3y = 5
   \]

2. **Isolate the \(y\)-term on one side:**
   \[
   3y = -2x + 5
   \]
   Subtract \(2x\) from both sides.

3. **Solve for \(y\) by dividing every term by 3:**
   \[
   y = -\frac{2}{3}x + \frac{5}{3}
   \]

### Slope-Intercept Form:
The slope-intercept form of the equation is:
\[
y = -\frac{2}{3}x + \frac{5}{3}
\]

In this form, the slope (\(m\)) is \(-\frac{2}{3}\) and the y-intercept (\(b\)) is \(\frac{5}{3}\).

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Would you like more details on this, or do you have any other questions?

Here are 5 related questions that you might find interesting:

1. How do you convert an equation from slope-intercept form to standard form?
2. What is the slope of the line perpendicular to \(y = -\frac{2}{3}x + \frac{5}{3}\)?
3. How do you find the x-intercept of the line \(2x + 3y = 5\)?
4. What is the meaning of the slope and y-intercept in the context of a real-world problem?
5. How do you graph a line given its equation in slope-intercept form?

**Tip:** When converting equations, carefully isolate the variable of interest by performing inverse operations systematically.

Learn how to convert the equation 2x + 3y = 5 from standard form (Ax + By = C) into slope-intercept form (y = mx + b) with a detailed step-by-step solution. This problem covers key algebraic concepts, including linear equations and the slope-intercept form. Suitable for students in Grades 7-9.

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