The flag-down fare of a taxi is $3. Given that a passenger is charged $0.50 for each kilometer the taxi travels, find the amount of money the passenger has to pay if the taxi covers a distance of
(i) 3 km,
(ii) 6 km,
(iii) 10 km.
Given that $y represents the amount of money a passenger has to pay if the taxi travels $x km, copy and complete the table.
| x | 3 | 6 | 10 |
|---|---|---|----|
| y | | | |
On a sheet of graph paper, using a scale of 1 cm to represent 1 km on the horizontal axis and 2 cm to represent $1 on the vertical axis, plot the pairs of values of (x, y).
Answer (2)
To calculate taxi fares, we use the formula y = 3 + 0.50 x , where y is the fare and x is the distance in kilometers. For distances of 3 km, 6 km, and 10 km, the fares are $4.50, $6.00, and $8.00 respectively. This relationship can be plotted on a graph showing a linear connection between distance and fare.
;
Calculate the fare for 3 km: y = 3 + 0.50 × 3 = 4.5 .
Calculate the fare for 6 km: y = 3 + 0.50 × 6 = 6 .
Calculate the fare for 10 km: y = 3 + 0.50 × 10 = 8 .
The fares are $4.50 , $6.00 , and $8.00 for 3 km, 6 km, and 10 km, respectively. The relationship can be plotted on a graph. The table is completed and the graph can be plotted with the points (3, 4.5), (6, 6) and (10, 8).
Explanation
Problem Analysis Let's analyze the problem. The taxi fare consists of a fixed flag-down fare and a variable charge per kilometer. We need to calculate the total fare for different distances, complete a table, and plot the corresponding points on a graph.
Cost Function The total cost, y , can be expressed as a function of the distance, x , using the equation: y = 3 + 0.50 x
Calculating the Fares Now, let's calculate the fare for each given distance: (i) For x = 3 km: y = 3 + 0.50 × 3 = 3 + 1.5 = 4.5 So, the fare for 3 km is $4.50 .
(ii) For x = 6 km: y = 3 + 0.50 × 6 = 3 + 3 = 6 So, the fare for 6 km is $6.00 .
(iii) For x = 10 km: y = 3 + 0.50 × 10 = 3 + 5 = 8 So, the fare for 10 km is $8.00 .
Completing the Table Now, let's complete the table:
x (km)
3
6
10
y (\)
4.5
6
8
Plotting the Graph Finally, we plot the points (3, 4.5), (6, 6), and (10, 8) on a graph. The x-axis represents the distance in km, and the y-axis represents the amount to pay in dollars. The scale is 1 cm to represent 1 km on the horizontal axis and 2 cm to represent $1 on the vertical axis. The points lie on a straight line, which represents the linear relationship between the distance and the total fare.
Examples
Taxis use a base fare plus a per-kilometer charge. This is a linear relationship, just like calculating the cost of a phone plan with a monthly fee plus per-minute charges. Understanding this helps you estimate travel costs or compare different service plans. For example, if you know the base fare and per-kilometer charge of two taxi companies, you can calculate which one is cheaper for different distances.
