NCERT Class 9 Solutions: Linear Equation in Two Variable (Chapter 4) Exercise 4.3 – Part-3

Q-4 The taxi fare in a city is as follows: For the first kilometer, the fare is Rs. 8 and for the subsequent distance it is Rs. 5 per kilometer. Taking the distance covered as x km and total fares as Rs. y, write a linear equation for this information, and draw its graph.

Solution:

Given,

Taxi fare for subsequent distance Equation Rs. 5

Let,

  • Total distance covered Equation

  • Total fare Equation

According to problem,

  • Taxi fare for first kilometer Equation Rs. 8

  • If the total distance is x, fare for rest of the Equation kilometer ( at the rate of Rs. 5 per km) Equation

  • Since the fare for first kilometer = Rs. 8, so, the total fare Equation

    Equation

    Equation

    Equation

    Hence, Equation is the required linear equation

Drawing the Graph

We can draw the graph by finding two points on this equation and drawing a line joining those points.

The equation is

Equation …………….equation (1)

Now, putting the value Equation in equation (1)

Equation

Equation So the solution is Equation this is first point (the y intercept)

Putting the value Equation in equation (1)

Equation

Equation . So the solution is Equation this is the second point

Segment f Segment f: Segment [C3, C2] Point C2 Point C2: (A2, B2) Point C2 Point C2: (A2, B2) Point C2 Point C2: (A2, B2) Point C3 Point C3: (A3, B3) Point C3 Point C3: (A3, B3) Point C3 Point C3: (A3, B3) (0,3) text2 = "(0,3)" (1,8) text1 = "(1,8)" y=5x 3 text3 = "y=5x 3"

Graph for Equation Y = 5x + 3

x-axis and y-axis, distance covered as x km and total fare as Rs. Y. Equation is y = 5x + 3

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