We are given the equation:

\[
\frac{2}{3}x + \frac{3}{4}y = \frac{3}{2}
\]

Our task is to express this in the slope-intercept form, \(y = mx + c\), where \(m\) is the slope and \(c\) is the y-intercept.

### Step 1: Isolate \(y\) on one side

We start by isolating the \(y\)-term on the left-hand side. First, subtract \(\frac{2}{3}x\) from both sides:

\[
\frac{3}{4}y = -\frac{2}{3}x + \frac{3}{2}
\]

### Step 2: Solve for \(y\)

Next, multiply both sides of the equation by \(\frac{4}{3}\) to eliminate the fraction in front of \(y\):

\[
y = \frac{4}{3}\left(-\frac{2}{3}x + \frac{3}{2}\right)
\]

Now, distribute the \(\frac{4}{3}\) across the terms inside the parentheses:

\[
y = \left(\frac{4}{3} \cdot -\frac{2}{3}\right)x + \left(\frac{4}{3} \cdot \frac{3}{2}\right)
\]

Simplify each term:

\[
y = -\frac{8}{9}x + 2
\]

### Step 3: Identify \(m\) and \(c\)

Now that the equation is in the form \(y = mx + c\):

- The slope \(m = -\frac{8}{9}\)
- The y-intercept \(c = 2\)

### Final Answer:
- \(m = -\frac{8}{9}\)
- \(c = 2\)

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Would you like more details or have any questions?

Here are some related questions to explore:

1. How do you find the slope given two points?
2. What is the general method for converting a linear equation to slope-intercept form?
3. How can you determine the x-intercept from this equation?
4. What does the slope of a line represent geometrically?
5. How can we verify the solution by graphing?

**Tip:** When converting to slope-intercept form, always aim to isolate \(y\) first for clarity!

Learn how to find the slope and y-intercept of the linear equation 2/3x + 3/4y = 1 1/2 by converting it to slope-intercept form. This step-by-step solution involves isolating y and simplifying the equation to y = mx + c. Suitable for students in Grades 8-10.

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