John tells his daughter, ‘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.” Represent this situation algebraically and graphically.

Let the present age of father be x and present age of daughter be y.

John tells his daughter, ‘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.”

∴ x – 7 = 7(y – 7)

⇒ x – 7 = 7y – 49

⇒ x – 7y + 42 = 0

⇒ x = 7y – 42

⇒ x = 7(y – 6) …[1]

The coordinates satisfying above equation are

Also, x + 3 = 3(y + 3)

⇒ x + 3 = 3y + 9

⇒ x – 3y – 6 = 0

⇒ x = 3y + 6

⇒ x = 3(y + 2) …[2]

The graph of both the equation is the required graphical representation and the equations [1] and [2] are two required algebraic representations.