the taxi fare in the city is follows for the first kilometre the fare rupees 8 and for the screen distant it is rupees 5 per kilometre taking the distance covered as X km and total fare as rupees why write a linear equation for the information and draw its graph
Answers
Answer:
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