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 satisfies this data. (You may take their contributions as Rs. X and Rs. Y) Draw the graph of the same.

Answer 1

Hint:First assume the given notations for the contributions and then assign the equation with the given condition. Compare the equation with standard forms of different types of equations. Then use the boundary condition to get the intercepts of the equation and then draw it on a graph.

Complete step by step answer:
To form the equation from given data we will assume the given notations to the conditions given in the problem, therefore
We will assume
Contribution of Yamini in the relief fund = Rs. x ……………………………………. (1)
Contribution of Fatima in the relief fund = Rs. y ……………………………………. (2)
As per the condition given in the problem i.e. Yamini and Fatima together contributed Rs. 100 for the Prime Minister’s Relief Fund to help the earthquake victims.
By using the given condition, equation (1) and equation (2) we can get the equation as,
Rs. x +Rs. y = Rs. 100
As the unit in the above equation is equal on the both sides of the equation therefore we can remove it. Therefore by removing the unit we will get,
x + y = 100 …………………………………………………………………………………………………. (3)
We can convert the above equation as follows,
y = - x + 100
If we compare the above equation with y = mx + c we can say that the above equation is the equation of straight line with slope m = -1.
To draw the graph of a given equation we will use the boundary conditions so that we can get the intercepts and draw a line through that.
Now, to get the intercepts we will put y = 0 in equation (1) therefore we will get,
x + 0 = 100
Therefore, x = 100
Assume the x – intercept as A, therefore,
A (100, 0)
Also, put x = 0 in equation (1) to get the y – intercept,
Therefore, 0 + y = 100
Therefore y = 100
Assume the y - intercept as B therefore,
B (0, 100)
Now if we plot the points A (100, 0) and B (0, 100) and draw a line through them we will get an equation of line x + y = 100. Therefore we will get,

Note: After drawing the graph you can cross check your answer by taking any two points on the line as $P({{x}_{1}},{{y}_{1}})$ and $Q({{x}_{2}},{{y}_{2}})$ and finding the slope of that line by using the formula \[m=\dfrac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}\]. If it is equal to -1 then your answer is correct.