The Auto Rickshaw fare in a city is charged Rs 10 for the first kilometer and @ Rs 4 per kilometer for subsequent distance covered. Write the linear equation to express the above statement. Draw the graph of the linear equation
Solution:
Given, an auto rickshaw fare in a city is Rs. 10 for the first kilometer and Rs. 4 per kilometer for subsequent distance covered.
We have to write the linear equation and draw the graph of the equation.
Let the total distance covered be x km
Let the total fare be Rs. y
Total fare = fare for the first kilometer + fare for the remaining distance
Remaining distance = x - 1
Fare for the remaining distance = 4(x - 1)
So, total fare = 10 + 4(x - 1)
= 10 + 4x - 4
Total fare = 6 + 4x
y = 6 + 4x
Therefore, the linear equation is y = 6 + 4x
When x = 0, y = 6 + 4(0) = 6
When x = -1, y = 6 + 4(-1) = 6 - 4 = 2
When x = -2, y = 6 + 4(-2) = 6 - 8 = -2
The points are (0, 6), (-1, 2) and (-2, -2)
On plotting the points and joining them,
We obtain a straight line which is the graph of the equation.
✦ Try This: A cab fare in a city is charged Rs 25 for the first kilometer and @ Rs 14 per kilometer for subsequent distance covered. Write the linear equation to express the above statement. Draw the graph of the linear equation.
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 4
NCERT Exemplar Class 9 Maths Exercise 4.4 Sample Problem 3
The Auto Rickshaw fare in a city is charged Rs 10 for the first kilometer and @ Rs 4 per kilometer for subsequent distance covered. Write the linear equation to express the above statement. Draw the graph of the linear equation
Summary:
The Auto Rickshaw fare in a city is charged Rs 10 for the first kilometer and @ Rs 4 per kilometer for subsequent distance covered. The linear equation to express the above statement is y = 6 + 4x. The graph of the linear equation is mentioned above
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