Ravish tells his daughter Aarushi, "Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be". If present ages of Aarushi and Ravish are x and y years respectively, represent this situation algebraically as well as graphically.
We are given the present age of Ravish as y years and Aarushi as x years.
Age of Ravish seven years ago = y - 7
Age of Aarushi seven years ago = x – 7
It has already been said by Ravish that seven years ago he was seven times old then Aarushi was then So, y - 7 = 7( x – 7)
y – 7 = 7x – 49
7x - y = - 7 + 49
7x – y – 42 = 0 .... (1)
Age of Ravish three years from now = y + 3
Age of Aarushi three years from now = x + 3
It has already been said by Ravish that three years from now he will be three times older then Aarushi will be then So, Y + 3 = 3 (x + 3)
y + 3 = 3x + 9
3x + 9 – y – 3 = 0
3x – y + 6 = 0 ..... (2)
(1) and (2) are the algebraic representation of the given statement.
We are given, 7x - y- 42 = 0
We get, y = 7x – 42
Now, substituting x = 0 in y = 7x – 42, we get y = – 42
Substituting x = 6 in y = 7x - 42, we get y = 0
Thus, we have the following table exhibiting the abscissa and ordinates of points on the line represented by the given equation
We are given, 3x – y + 6 = 0
We get, Y = 3x + 6
Now, substituting x = 0 in y = 3x + 6, We get y = 6
Substituting x = -2 in y = 3x + 6,
We get y = 0
Thus, we have the following table exhibiting the abscissa and ordinates of points on the line represented by the given equation
The red – line represents the equation 7x - y - 42 = 0.
The blue-line represents the equation 3x - y + 6 = 0.