Question

After 5 years, the age of the father will be two times the age of his son. Write a linear equation in two variables to represent this statement and also draw the graph.
(A) $ x = 2y + 5 $
(B) $ x = 2y - 5 $
(C) $ x - 2y = - 5 $
(D) $ x = y + 5 $

Answer 1

Hint: Consider the age of the father to be one variable and the age of the son to be another variable. The convert the word problem into a mathematical equation. It would be a linear equation as its degree would be 1. You can draw the graph by plotting points that satisfy the equation and then joining them in a straight line.

Complete step-by-step answer:
Here we have to consider the father’s and son’s age.
Let the present age of the father be $ y $
And the present age of son be $ x $
Then after five years,
The age of father will be $ y + 5 $
And the age of son will be $ x + 5 $
It is given that, after $ 5 $ years the age of the father will be two times the age of his son.
Mathematically we can write it as
 $ x + 5 = 2(y + 5) $
 $ \Rightarrow x + 5 = 2y + 10 $
Rearranging it, we get
 $ x = 2y + 5 $
 $ \therefore $ The required linear equation to represent the above statement is $ x = 2y + 5 $
Therefore, from the above explanation, the correct answer is, option (A) $ x = 2y + 5 $
Now, we have to draw the graph of the above linear equation.
Our given equation is $ x = 2y + 5 $
To draw the required graph, we need to find at least two values of $ (x,y) $ that satisfy the above linear equation.
Let us consider $ x = 0 $
Then, $ x = 2(y) + 5 $
 $ \Rightarrow 0 = 2(y) + 5 $
 $ \Rightarrow 0 - 5 = 2y $
Dividing both the sides by $ 2 $
 $ \Rightarrow y = \dfrac{{ - 5}}{2} $
 $ \Rightarrow y = - 2.5 $
Thus, we got one coordinate point as $ A(0, - 2.5) $
Now put $ y = 0 $ in the given linear equation.
 $ x = 2y + 5 $ [The given equation]
 $ \Rightarrow x = 2(0) + 5 $
 $ \Rightarrow x = (0) + 5 $
 $ \Rightarrow x = 5 $
Thus the second coordinate point is $ B(5,0) $
Now we draw the graph.
For that, mark these two coordinate points on the graph paper and then join the points with the ruler.
Refer the following diagram

So, the correct answer is “Option A”.

Note: It is possible that you consider the age of father to be $ x $ and the age of son to be $ y $ . In that case, your answer would be $ y = 2x + 5 $ . This doesn’t mean your answer is wrong. You just need to understand that the variables taken by you are different than the variables considered in the options. If this happens, then simple interchange $ x $ and $ y $ . And you will get the required answer.