Let’s solve this step by step.
We are told:
> The cost of a taxi ride is $3.00 plus $0.75 for every 0.5 km.
We need to represent this relationship in:
1. A
Table of Values (up to 10 km)
2. An
Equation
3. A
Graph (we’ll describe how to draw it, since we can’t actually draw here)
---
Step 1: Understand the rate
It says “$0.75 for every 0.5 km”.
That means for
each full kilometer, you pay twice that amount:
→ $0.75 × 2 =
$1.50 per km
So the cost increases by $1.50 for each additional kilometer.
Plus, there’s a flat fee of $3.00 — that’s the starting cost even if you go 0 km.
---
Step 2: Write the equation
Let:
- C = total cost ($)
- d = distance traveled (km)
Then:
>
C = 1.5d + 3
✔ This matches the pattern: start at $3, add $1.50 for each km.
---
Step 3: Make a Table of Values (up to 10 km)
We’ll calculate cost for d = 0, 1, 2, ..., up to 10.
Use formula: C = 1.5d + 3
| Distance (km) | Cost ($) |
|---------------|------------------|
| 0 | 1.5(0) + 3 = 3 |
| 1 | 1.5(1) + 3 = 4.5 |
| 2 | 1.5(2) + 3 = 6 |
| 3 | 1.5(3) + 3 = 7.5 |
| 4 | 1.5(4) + 3 = 9 |
| 5 | 1.5(5) + 3 = 10.5|
| 6 | 1.5(6) + 3 = 12 |
| 7 | 1.5(7) + 3 = 13.5|
| 8 | 1.5(8) + 3 = 15 |
| 9 | 1.5(9) + 3 = 16.5|
| 10 | 1.5(10)+3 = 18 |
You can write this table with two columns: Distance and Cost.
---
Step 4: Graph
To graph this:
- Put
Distance (km) on the x-axis (horizontal)
- Put
Cost ($) on the y-axis (vertical)
- Plot points from the table: (0,3), (1,4.5), (2,6), (3,7.5), ..., (10,18)
- Connect them with a straight line — because it’s linear!
The line will start at (0,3) and go up steadily — rising $1.50 for every 1 km right.
---
Final Check:
Does the equation match the description?
Original: $3 base + $0.75 per 0.5 km → which is $1.50 per km → yes, C = 1.5d + 3 ✔️
Table values correct? Let’s spot-check:
At d=2: 1.5×2=3 +3=6 ✔️
At d=10: 1.5×10=15 +3=18 ✔️
All good.
---
Final Answer:
Equation:
C = 1.5d + 3
Table of Values (up to 10 km):
| Distance (km) | Cost ($) |
|---------------|----------|
| 0 | 3.0 |
| 1 | 4.5 |
| 2 | 6.0 |
| 3 | 7.5 |
| 4 | 9.0 |
| 5 | 10.5 |
| 6 | 12.0 |
| 7 | 13.5 |
| 8 | 15.0 |
| 9 | 16.5 |
| 10 | 18.0 |
Graph:
Plot the points from the table on a coordinate plane with Distance (km) on the x-axis and Cost ($) on the y-axis. Draw a straight line through all the points. The line starts at (0, 3) and rises 1.5 units vertically for every 1 unit horizontally.
Parent Tip: Review the logic above to help your child master the concept of linear relations worksheet.
