Answer

Verified

412.5k+ views

**Hint**: In order to draw the graph for any line equation, the best possible way is to find the two coordinates and join those two points. This way we can easily get the graph. In order to get the coordinates, we need to take the following two steps: (i) replace $ y=0 $ in the given equation and find the coordinates of a point (ii) replace $ x=0 $ in the given equation and find the coordinates of the other point. Here, we will follow the same trick, firstly we will find the coordinates of the two points using the tricks mentioned in (i) and (ii) and connect the points which will give us the required graph.

**:**

__Complete step-by-step answer__Here, we have to find the graph of the given line equation $ x-2y=3......................(i) $ . Now, we will replace the value of x and y with ‘zero’, one by one, and find the required two coordinates, i. e., point A and point B (let us say).

Replacing the value of x with ‘zero’ in equation (i), we get,

$ \Rightarrow 0-2y=3 $

$ \Rightarrow -2y=3 $

$ \Rightarrow 2y=-3 $

$ \therefore y=\dfrac{-3}{2} $

Hence when $ x=0 $ in the above equation (i), the value of y is $ -\dfrac{3}{2} $ . So, the point is $ \text{A}\left( 0,\dfrac{-3}{2} \right) $ .

Similarly, now, we place the value of y with ‘zero’ in the above equation (i), we get,

$ \Rightarrow x-2\times 0=3 $

$ \Rightarrow x-0=3 $

$ \therefore x=3 $

Hence when $ y=0 $ in the above equation (i), the value of x is 3. So, the point is $ \text{B}\left( 3,0 \right) $ .

Now, we need to plot these points $ \text{A}\left( 0,\dfrac{-3}{2} \right) $ and $ \text{B}\left( 3,0 \right) $ in the x – y plane and join these points, in order to obtain the required graph for the equation $ x-2y=3 $ .

Now, to find the coordinates of the point under a given condition, we need to simply replace that value in the given equation (i), so

(i) Replace the value of x with -5 in the given equation (i), we get,

$ \Rightarrow -5-2y=3 $

$ \Rightarrow -2y=3+5 $

$ \Rightarrow -2y=8 $

$ \Rightarrow 2y=-8 $

$ \Rightarrow y=\dfrac{-8}{2} $

$ \therefore y=-4 $

Hence when $ x=-5 $ in the above equation (i), the value of y is -4. So, the required coordinates of point are $ \left( -5,-4 \right) $ .

(ii) Replace the value of y with 0 in the given equation (i), we get,

$ \Rightarrow x-2\times 0=3 $

$ \Rightarrow x-0=3 $

$ \therefore x=3 $

Hence when $ y=0 $ in the above equation (i), the value of x is 3. So, the required coordinates of point are $ \left( 3,0 \right) $ .

**So, the correct answer is “Option A”.**

**Note**: Students normally make a mistake while replacing the values in the equation and solving the equation and also while plotting the point in the graph. One other alternate method, to find the coordinates at some given condition is to simply solve the given condition and the given equation as shown below:

(i) when $ x=-5 $ , we simply need to solve this equation and equation (i),

$ x-2y=3............(ii) $

$ x=-5........(iii) $

Now, subtracting equation (iii) from (ii), we get,

$ \begin{align}

& x-2y=3 \\

& -x-0y=5 \\

& \underline{\text{ }} \\

& -2y=8 \\

\end{align} $

$ \Rightarrow 2y=-8 $

$ \Rightarrow y=\dfrac{-8}{2} $

$ \Rightarrow y=-4 $

Hence when $ x=-5 $ in the above equation (i), the value of y is -4. So, the required coordinates of point are $ \left( -5,-4 \right) $ .

(i) when $ y=0 $ , we simply need to solve this equation and equation (i),

$ x-2y=3............(ii) $

$ y=0........(iii) $

Now, multiplying equation (iii) by 2, we get,

$ 2y=0..............(iv) $

Adding equation (ii) from (iv), we get,

$ \begin{align}

& x-2y=3 \\

& 0x+2y=0 \\

& \underline{\text{ }} \\

& x=3 \\

\end{align} $

Hence when $ y=0 $ in the above equation (i), the value of x is 3. So, the required coordinates of point are $ \left( 3,0 \right) $ .

Recently Updated Pages

The base of a right prism is a pentagon whose sides class 10 maths CBSE

A die is thrown Find the probability that the number class 10 maths CBSE

A mans age is six times the age of his son In six years class 10 maths CBSE

A started a business with Rs 21000 and is joined afterwards class 10 maths CBSE

Aasifbhai bought a refrigerator at Rs 10000 After some class 10 maths CBSE

Give a brief history of the mathematician Pythagoras class 10 maths CBSE

Trending doubts

Difference Between Plant Cell and Animal Cell

Give 10 examples for herbs , shrubs , climbers , creepers

Name 10 Living and Non living things class 9 biology CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Write a letter to the principal requesting him to grant class 10 english CBSE

Fill the blanks with proper collective nouns 1 A of class 10 english CBSE

Write the 6 fundamental rights of India and explain in detail