To sketch the graph of the equation \( 3x + 2y = 1 \), follow these steps:

### 1. Rearrange the equation to slope-intercept form:
The slope-intercept form of a line is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

Start with:
\[
3x + 2y = 1
\]

Solve for \( y \):
\[
2y = -3x + 1
\]

Now divide by 2:
\[
y = -\frac{3}{2}x + \frac{1}{2}
\]

This gives us the slope \( m = -\frac{3}{2} \) and the y-intercept \( b = \frac{1}{2} \).

### 2. Plot the y-intercept:
The y-intercept is where \( x = 0 \). So, the point \( (0, \frac{1}{2}) \) is on the graph.

### 3. Find the x-intercept:
To find the x-intercept, set \( y = 0 \) in the original equation:
\[
3x + 2(0) = 1
\]
\[
3x = 1
\]
\[
x = \frac{1}{3}
\]
So the x-intercept is \( \left( \frac{1}{3}, 0 \right) \).

### 4. Plot the x-intercept:
Plot the point \( \left( \frac{1}{3}, 0 \right) \) on the graph.

### 5. Draw the line:
Now, draw a straight line through the points \( (0, \frac{1}{2}) \) and \( \left( \frac{1}{3}, 0 \right) \).

Would you like me to generate the graph for this equation?

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Here are 5 follow-up questions:

1. How would the graph change if the slope were positive instead of negative?
2. What does the slope of this line tell you about its steepness and direction?
3. How do you find the x- and y-intercepts of more complex equations?
4. What happens if you change the constant on the right-hand side of the equation?
5. How do you determine if two lines are parallel based on their equations?

**Tip:** The slope-intercept form \( y = mx + b \) makes it easy to graph linear equations because the slope and intercept are clearly visible.

Learn how to sketch the graph of the linear equation 3x + 2y = 1 by converting it into slope-intercept form and finding the intercepts. This tutorial covers algebraic concepts, including slope and intercept, suitable for students in Grades 7-9.

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