https://file.aiquickdraw.com/mathbot/file/1726600532279y8thj47h.jpg

Let's analyze the given linear equation: 

\[
3x - 2y = 6
\]

### Step 1: Rearrange to slope-intercept form (\(y = mx + b\)):

Start by solving for \(y\):

\[
3x - 2y = 6
\]
Subtract \(3x\) from both sides:
\[
-2y = -3x + 6
\]
Now divide by \(-2\) to isolate \(y\):
\[
y = \frac{3}{2}x - 3
\]

### Step 2: Identify the slope and y-intercept:

- **Slope (m)**: \( \frac{3}{2} \)
- **Y-intercept (b)**: \(-3\)

### Step 3: Plot the graph:

- The line crosses the y-axis at \((0, -3)\).
- Use the slope \( \frac{3}{2} \), which means for every 2 units to the right, move 3 units up.

### Step 4: Match with the options:

Looking at the options in the image:
- **Option D** shows the correct line with a positive slope and a y-intercept at \(-3\).

Thus, the correct answer is **Option D**.

Would you like further details on how to graph it manually or any other related questions?

### Relative questions:
1. What is the importance of slope-intercept form in graphing linear equations?
2. How do you find the x-intercept of a line given in standard form?
3. Can every linear equation be written in slope-intercept form?
4. How would the graph of the equation change if the slope were negative?
5. How do you graph a line if it's given in point-slope form?

### Tip:
Always verify the slope and intercept visually when matching graphs to equations.

Ms. Molina asked her students to graph the linear function 3x - 2y = 6. Which graph corresponds to this equation?

Learn how to graph the linear function 3x - 2y = 6 with step-by-step instructions. Understand how to rearrange the equation into slope-intercept form and use the slope and y-intercept to plot the graph. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation