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When making the graph of the possible jet skiing locations, draw all four cost equations (one for Carlsbad, one for Oceanside, and two for Dana Point (AM vs PM hours)) on the same coordinate plane.  Make sure to choose appropriate data scaling and clearly label the axes with units being used.

Since the jet ski cost equations are linear equations, it might be helpful to put each equation into slope-intercept form (y = mx + b) for ease of graphing.  .  Graph all the jet ski cost equations on the same coordinate plane. Graphs must be original and not made on a calculator or computer.  Label the axes with appropriate descriptions (units) and scales. Identify the points of intersections if they exist.The graph compares the total costs across different jet ski locations for various hours.

The x-axis represents the number of hours h*h*.

The y-axis represents the total cost in dollars.

To graph the jet ski cost equations for the different locations on the same coordinate plane, let's start by reviewing the simplified equations:

1. **Carlsbad**: $ C(h) = 28 + 75h $
2. **Oceanside**: $ C(h) = 67.68 + 60h $
3. **Dana Point (AM)**: $ C(h) = 16.36 + 90h $
4. **Dana Point (PM)**: $ C(h) = 16.36 + 110h $

### **Graphing Instructions:**

- **X-Axis**: Number of hours $ h $. 
  - Label as "Hours (h)".
  - Choose an appropriate scale, perhaps from 0 to 10 hours.
  
- **Y-Axis**: Total Cost in dollars.
  - Label as "Total Cost (\$)".
  - The y-axis will vary significantly due to different starting costs and hourly rates. A scale from $0 to $1000 should suffice.

### **Graphing Steps**:
1. **Plotting the y-intercept**: 
   - For Carlsbad, the y-intercept is $28.
   - For Oceanside, it is $67.68.
   - For Dana Point (AM) and (PM), it is $16.36.

2. **Plotting the slope (m)**:
   - Carlsbad has a slope of 75, so for each additional hour, the cost increases by $75.
   - Oceanside has a slope of 60, so for each additional hour, the cost increases by $60.
   - Dana Point (AM) has a slope of 90.
   - Dana Point (PM) has a slope of 110.

3. **Plot each equation** on the coordinate plane by starting at the y-intercept and following the slope.

4. **Label the points of intersection** (if any), which would show at what point the cost of renting at different locations would be the same.

### **Intersection Points**:
- Solve for $ h $ where two equations equal each other to find the intersection points.

Would you like a detailed explanation on solving for intersection points or guidance on how to hand-draw this graph? Also, I can assist in creating a digital version of this graph if you prefer. 

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### **Relative Questions**:
1. What does the slope represent in these cost equations?
2. How would the graph change if the cost per hour at Carlsbad increased?
3. What is the significance of the y-intercept in each equation?
4. Which location becomes cheaper after 5 hours of rental?
5. How do the rates compare between Dana Point (AM) and Dana Point (PM)?
6. How does the initial cost affect the overall comparison for shorter rental periods?
7. Can you explain how to calculate the exact intersection points for any two given cost equations?
8. What additional costs might alter the cost equations or graph interpretation?

### **Tip**:
When graphing linear equations, always check the scales of your axes. Proper scaling ensures that important details like intersection points are clearly visible.

Learn how to graph linear equations representing jet ski rental costs for Carlsbad, Oceanside, and Dana Point (AM & PM). Understand the concepts of slope, intercepts, and intersection points. Explore cost comparisons across different locations and hours of rental.

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