Let’s solve both problems step by step — “Cell Phone Charges” and “Plumber”.
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Problem 1: Cell Phone Charges
We’re told:
- There is a
flat rate of $20 per month.
- Plus, there’s an
additional charge for each minute used.
- From the table:
- At 5 minutes → total cost = $25
- At 10 minutes → total cost = $30
- At 15 minutes → total cost = $35
So, let’s find how much they charge per minute.
From 5 to 10 minutes (that’s +5 minutes), cost goes from $25 to $30 → that’s +$5.
So, $5 for 5 minutes →
$1 per minute.
Check with next row: 10 to 15 minutes (+5 min) → $30 to $35 (+$5). Same thing.
So, equation should be:
> Total Cost = Flat Rate + (Cost per Minute × Minutes Used)
> y = 20 + 1·x
> or simply:
y = x + 20
Now check coordinates given in graph section:
- (5, 25): plug in x=5 → y=5+20=25
✔
- (10, 30): 10+20=30
✔
- (15, 35): 15+20=35
✔
Perfect.
Equation:
y = x + 20
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Problem 2: Plumber
Given:
- Flat rate = $40 just to come out.
- Then charges per hour worked.
- Table shows:
- 1 hour → $75
- 2 hours → $110
- 3 hours → $145
Find hourly rate.
From 1 to 2 hours (+1 hr), cost goes from $75 to $110 → +$35
From 2 to 3 hours (+1 hr), $110 to $145 → +$35
So,
$35 per hour.
Equation:
> Total Cost = Flat Rate + (Hourly Rate × Hours Worked)
> y = 40 + 35x
Check with table:
- x=1 → y=40+35(1)=75
✔
- x=2 → 40+70=110
✔
- x=3 → 40+105=145
✔
Coordinates listed: (1,75), (2,110), (3,145) — all match.
Equation:
y = 35x + 40
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Final Answer:
For Cell Phone Charges:
y = x + 20
For Plumber:
y = 35x + 40
Parent Tip: Review the logic above to help your child master the concept of algebraic rules tables and graph worksheet.
