To sketch the graph of the equation \( 4y - 3x = 12 \) on a grid, let's follow these steps:

### Step 1: Convert to Slope-Intercept Form
The slope-intercept form of a linear equation is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept. To convert \( 4y - 3x = 12 \) to this form:

\[
4y = 3x + 12
\]

Now, divide everything by 4 to solve for \( y \):

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

This equation tells us that the slope \( m \) is \( \frac{3}{4} \), and the y-intercept \( b \) is 3.

### Step 2: Plot the Y-Intercept
The y-intercept is the point where the line crosses the y-axis. For \( b = 3 \), this is the point \( (0, 3) \).

### Step 3: Use the Slope to Find Another Point
The slope \( \frac{3}{4} \) means that for every 4 units you move to the right (along the x-axis), you move 3 units up (along the y-axis). Starting from the y-intercept \( (0, 3) \), if you move 4 units to the right, you end up at \( x = 4 \). Moving 3 units up from 3, you reach \( y = 6 \). So another point on the line is \( (4, 6) \).

### Step 4: Draw the Line
Now, you can draw a straight line through the points \( (0, 3) \) and \( (4, 6) \). This line represents the graph of the equation \( 4y - 3x = 12 \).

Would you like a detailed graph illustration, or do you have any questions?

Here are 5 related questions to consider:

1. How would the graph change if the slope were negative?
2. What is the significance of the slope and y-intercept in a real-world context?
3. How can you find the x-intercept of the equation \( 4y - 3x = 12 \)?
4. What happens to the graph if the constant term changes, e.g., \( 4y - 3x = 8 \)?
5. How can you graph the line using the intercepts method instead?

**Tip:** When graphing a line, always check the slope's direction to ensure accuracy.

Learn how to sketch the graph of the linear equation 4y - 3x = 12 on a grid. This problem covers concepts such as linear equations and graphing techniques. Suitable for students in Grades 7-9.

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