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!