To graph the equation $y = \frac{2}{5}x + 3$, follow these steps:

1. Identify the slope and y-intercept:

   • The equation is in the slope-intercept form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.
   • Here, $m = \frac{2}{5}$ and $b = 3$. This means the slope is $\frac{2}{5}$ and the y-intercept is $3$.

2. Plot the y-intercept:

   • Start by plotting the point $(0, 3)$ on the y-axis.

3. Use the slope:

   • The slope $\frac{2}{5}$ means "rise 2 units and run 5 units."
   • From the point $(0, 3)$, move 2 units up and 5 units to the right to get the point $(5, 5)$.
   • Plot this point.

4. Draw the line:

   • Connect the points $(0, 3)$ and $(5, 5)$ with a straight line.
   • Extend the line in both directions.

This graph shows a straight line with a gradual slope, passing through the y-intercept at $y = 3$.

Would you like a visual representation of this graph, or any further details?

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Here are 5 related questions for further exploration:

1. How would the graph change if the slope were negative, such as $y = -\frac{2}{5}x + 3$?
2. What is the x-intercept of this line?
3. How would you graph $y = \frac{2}{5}x - 1$?
4. How can you verify the slope and y-intercept using two points on the line?
5. What would the line look like if the slope were zero, like $y = 3$?

Tip: Always start graphing by plotting the y-intercept, as it's an easy reference point.