The equation given is $y = \frac{3}{2}x + 3$, which is in slope-intercept form, $y = mx + b$, where:

• $m = \frac{3}{2}$ is the slope.
• $b = 3$ is the y-intercept.

To graph this line:

1. Start with the y-intercept: The point where the line crosses the y-axis is at $(0, 3)$. So, plot the point $(0, 3)$ on the graph.

2. Use the slope: The slope $\frac{3}{2}$ means "rise over run," which translates to:

   • From the y-intercept $(0, 3)$, move 3 units up (positive rise) and 2 units to the right (positive run) to get the next point, which is at $(2, 6)$. Plot the point $(2, 6)$.

3. Plot more points if needed: For accuracy, repeat this process starting from the y-intercept and moving along the slope:

   • You could also move in the opposite direction (3 units down and 2 units left) to plot the point $(-2, 0)$.

4. Draw the line: Connect these points with a straight line to complete the graph of the equation.

Would you like me to create a visual graph for you based on these points? Let me know if you need more details.

Here are some related questions for practice:

1. What happens to the graph if the slope changes to $\frac{5}{2}$?
2. How would you graph $y = -\frac{3}{2}x + 3$?
3. What is the x-intercept of the line $y = \frac{3}{2}x + 3$?
4. How does changing the y-intercept affect the position of the line?
5. How would the line change if the slope were zero?

Tip: The slope defines the angle of inclination of the line, while the y-intercept fixes where it crosses the y-axis.