In this problem, you are asked to create graphs of linear relationships with different y-intercepts and specific slopes of $\frac{1}{5}$, $\frac{3}{5}$, and $\frac{6}{5}$.

To do this, the general equation of a line, which is $y = mx + b$, can be used. Here:

• $m$ represents the slope,
• $b$ represents the y-intercept.

Steps to Graph Each Line:

1. First Line with slope $\frac{1}{5}$:

   • Choose one of the y-intercepts (points on the y-axis). For example, pick the red point at $(0, 12)$.
   • Use the slope $\frac{1}{5}$, which means for every 5 units you move to the right (on the x-axis), move 1 unit up (on the y-axis).
   • Plot the next point by moving right 5 units and up 1 unit.

2. Second Line with slope $\frac{3}{5}$:

   • Pick a different y-intercept (e.g., the gray point at $(0, 8)$).
   • Use the slope $\frac{3}{5}$, which means for every 5 units you move to the right, move 3 units up.
   • Plot the next point accordingly.

3. Third Line with slope $\frac{6}{5}$:

   • Select the third y-intercept (e.g., the purple point at $(0, 4)$).
   • Use the slope $\frac{6}{5}$, meaning for every 5 units to the right, move 6 units up.

By following these steps, you'll be able to create three different lines, each with a unique slope and starting point on the y-axis.

Do you need further explanation on graphing these lines, or any clarification on the concepts?

Here are 5 follow-up questions to explore this further:

1. What happens when you change the slope of a line to a negative value?
2. Can you explain how to determine the slope if you're given two points on a line?
3. How would the graph look if the slope was an integer instead of a fraction?
4. How does changing the y-intercept affect the position of the line?
5. How can you verify if two lines are parallel just by looking at their equations?

Tip: Always check that the slope matches the rise-over-run when plotting points on a graph.