To graph the equation \( y = \frac{2}{3}x + 6 \), follow these steps:

### 1. Identify the Slope and Y-Intercept
- **Slope (\(m\))**: The slope of the line is \( \frac{2}{3} \). This means that for every 3 units you move to the right (positive \(x\)-direction), the line goes up by 2 units (positive \(y\)-direction).
- **Y-Intercept (\(b\))**: The y-intercept is 6. This is the point where the line crosses the y-axis. In this case, the line crosses the y-axis at \( (0, 6) \).

### 2. Plot the Y-Intercept
- Start by plotting the point \( (0, 6) \) on the graph.

### 3. Use the Slope to Find Another Point
- From \( (0, 6) \), move 3 units to the right and 2 units up. This gives you the point \( (3, 8) \).
- You can also move in the opposite direction: 3 units to the left and 2 units down, reaching \( (-3, 4) \).

### 4. Draw the Line
- Connect these points with a straight line, extending it in both directions.

### 5. Verify with a Few Points
- To ensure accuracy, you can substitute a few values of \(x\) into the equation to check that the corresponding \(y\) values lie on the line.

Would you like to see a visual representation or have further details? Here are 5 related questions to explore further:

1. How do you graph linear equations with different slopes?
2. What is the difference between positive and negative slopes in a graph?
3. How do you graph a line using the point-slope form of an equation?
4. How can you convert a linear equation from standard form to slope-intercept form?
5. How do you find the x-intercept of a linear equation?

**Tip:** When graphing linear equations, always start with the y-intercept and then use the slope to plot additional points!

Learn how to graph the linear equation y = 2/3x + 6 by identifying the slope and y-intercept, plotting points, and drawing the line. Perfect for students in Grades 8-10 learning about algebraic graphing techniques and slope-intercept form.

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