taxi fare in a city is as follows for the first kilometre the fare is rupees 8 in for the subsequent distance it is rupees 5 per kilometre taking the distance covered with X kilometre and total for rupees UAE write a linear equation for this information
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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 1st 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:
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
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 1st quadrant will be considered as they are positive.
Step-by-step explanation:
