Question

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 the given data will satisfy and also plot its graph.

Answer 1

Hint: We will first assume the amount both of them contributed individually as x and y. Then, substitute its sum to be equal to 100 according to the given data and thus we have the equation to plot the graph as well.

Complete step-by-step answer:
Let us assume that Yamini contributed Rs. x and Fatima contributed Rs. y for the earthquake victims in the Prime Minister’s relief fund. Since, we are given in the data in question that they both together contributed Rs. 100 for donation.
\[\therefore \] the total of both of their contributions must equal 100.
\[\therefore x + y = 100\]
Hence, we have the required equation as x + y = 100.
Let us draw its graph now:
The table given below will help us draw the graph:

x	100	0
y	0	100

$\therefore $ We have the required equation of the data in the question as: x + y = 100, where x is Yamini’s donation and y is Fatima’s donation in the Prime Minister’s relief fund for earthquake victims.

Note: The students must note that we have an equation in two variables here which are x and y, where x is the donation of one person and y being the donation of another person. We always plot an equation with two variables in the Cartesian plane.
The equation, we thus obtained which is x + y = 100, is known as a Linear Equation.
Linear equations are first order equations. The equations which give us a straight line are known as linear equations, like here we are getting a line passing through (100, 0) and (0, 100). This is a linear equation in two variables. We also have linear equations in one variable. For example: x = 20 and y = 5 are two examples of linear equations in one variable.