The taxi fare in a city is as follows: For the first kilometre, the fare is ₹ 8 and for the subsequent distance it is ₹ 5 per km. Taking the distance covered as x km and total fare as ₹ y, write a linear equation for this information, and draw its graph.
Solution:
Given: The distance covered is x km and the total fare is ₹ y. Also, the fare of the first kilometre is ₹ 8 and for the subsequent distance, it is ₹5 per km.
- Let the total distance covered = x km
- Therefore, subsequent distance = (x - 1) km
- The total fare covered = ₹ y
- Fare for the 1^{st} kilometre = ₹ 8
- Fare per km = ₹ 5
- Fare rate for the subsequent distance = 5(x - 1)
The linear equation for the above information is given by,
Total fare = Fare for the first kilometre + Subsequent distance × Fare per km
y = 8 + (x - 1) 5
y = 8 + 5x - 5
y = 5x + 3
5x - y + 3 = 0
This can be written as,
y = 5x + 3 --- Equation (1)
By substituting different values of x in Equation (1) we get different values for y.
- When x = 0, y = 5 × 0 + 3 = 0 + 3 = 3
- When x = 1, y = 5 × (1) + 3 = 5 + 3 = 8
- When x = 2, y = 5 × (2) + 3 = 10 + 3 = 13
- When x = -1, y = 5 × (-1) + 3 = -5 + 3 = -2
- When x = -2, y = 5 × (-2) + 3 = -10 + 3 = -7
Thus, we have the following table with all the obtained solutions:
x |
0 |
1 |
2 |
-1 |
-2 |
y |
3 |
8 |
13 |
-2 |
-7 |
By Plotting the points (0, 3), (1, 8), (2, 13), (-1, -2) and (-2, -7) on the graph paper and drawing a line joining them, we obtain the required graph.
The graph of the line represented by the given equation 5x - y + 3 = 0 is shown below:
Here, the variables x and y are representing the distance covered and the fare paid for that distance respectively, and these quantities cannot be negative.
Hence, only those values of x and y which are lying in the 1^{st} quadrant will be considered as they are positive.
Video Solution:
The taxi fare in a city is as follows: For the first kilometre, the fare is ₹ 8 and for the subsequent distance it is ₹ 5 per km. Taking the distance covered as x km and total fare as ₹ y, write a linear equation for this information, and draw its graph.
NCERT Solutions Class 9 Maths - Chapter 4 Exercise 4.3 Question 4:
Summary:
The linear equation for the taxi fare with the fare for the first-kilometre ₹ 8 and for the subsequent distance as ₹ 5 per km, x km distance covered, and total fare as ₹ y is 5x - y + 3 = 0 along with its graph shown.