The equation you provided is:

\[
3x + 2y - 1 = 0
\]

To rearrange it in the slope-intercept form \(y = mx + b\), follow these steps:

1. Move \(3x\) and \(-1\) to the other side of the equation:
   \[
   2y = -3x + 1
   \]

2. Divide the entire equation by 2 to solve for \(y\):
   \[
   y = -\frac{3}{2}x + \frac{1}{2}
   \]

Now, the equation is in the form \(y = mx + b\), where the slope \(m = -\frac{3}{2}\) and the y-intercept \(b = \frac{1}{2}\).

Would you like further details or have any questions?

Here are 5 related questions to explore this topic:

1. How do you find the slope from an equation in standard form?
2. What does the slope tell you about the graph of the line?
3. How can you find the x-intercept from this equation?
4. What is the significance of the y-intercept in a graph?
5. How do parallel and perpendicular lines relate to slopes?

**Tip:** To quickly identify the slope in an equation, always rearrange it to the form \(y = mx + b\).

Learn how to convert the linear equation 3x + 2y - 1 = 0 from standard form to slope-intercept form (y = mx + b). This problem covers key algebraic concepts, including identifying the slope and y-intercept, and is suitable for students in Grades 8-10.

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