Question: Part 1: Create a real-life situation related to you that can be represented by a linear function.
Example:
“A park charges ₱50 entrance fee plus ₱20 per hour of bicycle rental”
"A student starts with ₱100 savings and adds ₱50 every week. How much money will the student have after several weeks?"
Part 2: Write the Linear Function Equation
Linear function: y = 50x + 100
Where:
• (x) = number of weeks
• (y) = total savings
Part 3: Create a Table of Values
Complete the table for your linear function.
x (week/s) Y (total)
1 150
2 200
3 250
4 300
5 350
1. **State the problem:** A student starts with $100$ savings and adds $50$ every week. We want to find how much money the student will have after several weeks.
2. **Write the linear function:** The total savings $y$ after $x$ weeks can be modeled by the linear function:
$$y = 50x + 100$$
where $x$ is the number of weeks and $y$ is the total savings.
3. **Explain the formula:** The number $100$ is the initial amount of money the student has (the y-intercept).
The number $50$ is the amount added each week (the slope).
4. **Create a table of values:** Substitute $x = 1, 2, 3, 4, 5$ into the function to find $y$.
- For $x=1$: $$y = 50(1) + 100 = 50 + 100 = 150$$
- For $x=2$: $$y = 50(2) + 100 = 100 + 100 = 200$$
- For $x=3$: $$y = 50(3) + 100 = 150 + 100 = 250$$
- For $x=4$: $$y = 50(4) + 100 = 200 + 100 = 300$$
- For $x=5$: $$y = 50(5) + 100 = 250 + 100 = 350$$
5. **Summary table:**
| $x$ (weeks) | $y$ (total savings) |
|-------------|---------------------|
| 1 | 150 |
| 2 | 200 |
| 3 | 250 |
| 4 | 300 |
| 5 | 350 |
This table shows how the savings increase by $50$ every week starting from $100$.