NCERT Class 9 Solutions: Linear Equation In Two Variable (Chapter 4) Exercise 4.3 – Part 5

Graph of linear equation

Graph of a linear equation with points (0,1),(-3,-3)and (3,-1)

Graphy of a Linear Equation Is Straight Line

Graph of a linear equation with points (0,1),(-3,-3)and (3,-1)

Q-6 The work done by a body on application of a constant force is directly proportional to the distance travelled by the body. Express this in the form of an equation in two variables and draw the graph of the same by taking the constant force is 5 units. Read from the graph the work done when the distance traveled by the body is:

  1. 2 units

  2. 0 units

Solution:

Let x units be the distance traveled by the body and y units be the work done by constant force. yx . The equality is y=Fx , where F is the force. So if F = 5 than, according to question, y=5x

To draw the graph we find a few points on this equation.

  • Putting the value x=0 in the equation

    y=5x=0. So the solution is (0,0)

  • Putting the value x=1 in the equation

    y=5×1=5. So the solution is (1,5)

  • Putting the value x=2 in the equation

    y=5×2=10 . So the solution is (2,10)

Understand how y=5x passes through origin

Equation of Line Y=5x

Understand how y=5x passes through origin

  1. When x=2 units (distance), we read the graph above and find the value of y when the value of x is 2. The red line tell us where on our graph the x-coordinate is 2. Another line from that point to y axis tells us the corresponding value of y (green line). The corresponding y-coordinate is 10. This is the corresponding work done.

  2. When x=0 units (distance), we know the corresponding y-coordinate on our work-force graph is y = 0 (our line passes through 0, 0).

Q-7 Yamini and Fatima, two students of class IX of a school, together contributed Rs. 100 towards the Prime Minister’s Relief Fund, to help the earthquake victims. Write a linear equation which this data satisfies. (You may take their contributions as Rs. x and Rs. y ). Draw the graph of the same.

Solution:

The idea is that we know their total contribution to be 100 but not individual contribution. Therefore, if the contribution of Yamini is x and that of Fatima is y . Then, x+y=100 . We will again draw the graph by finding a few points.

  • Putting the value x=0

    0+y=100

    y=100 . So one point is (0,100)

  • Putting the value x=50

    50+y=100,

    y=10050

    y=50 . So another point is (50,50)

  • Putting the value x=100

    100+y=100,

    Or, y=100100

    y=0 . So the point is (100,0)

See how all coordinates of all points on this graph add to 100!

Graphy of equation x + y = 100

Coordinates of Any Point on This Graph Add to 100

Graphy of equation x + y = 100

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