Question

Draw the graph of each of the following linear equations in two variables:
(i) x+y=4
(ii) x-y=2
(iii) y=3x
(iv) 3=2x+y

Answer 1

Hint: In this question it is given that we have to draw the graph of the given linear equations, so for drawing a graph of each of the given linear equations we need to find at least two coordinates which satisfies the equations.

Complete step-by-step solution:
(i) First of all we are solving for (i)
x+y=4…………………..equation(1)
So for this, we have to find two coordinates which satisfies the above equation, so for coordinate i.e, (x,y) we have to first assume any value of x and by putting that value in the equation(1) we will get the value of y.
Let, x=0, now by putting this value in equation(1), we get,
   0+y=4
$\Rightarrow$y=4,
So our first coordinate is (0,4).
Now again let x=4, now by putting this value in equation(1), we get,
    4+y=4
$\Rightarrow$y=4-4
$\Rightarrow$y=0,
So another coordinate is (4,0).
Now we will place these points (0,4) and (4,0) on a graph sheet and by joining those two points by a scale we will get our required graph of x+y=4.

(ii) Now for equation (ii) which is,
x-y=2………………..equation(2)
In this case also we have to find two coordinates,
Let x=0, now by putting the value of x in equation(2), we get,
   0 - y = 2
$\Rightarrow$ -y=2
$\Rightarrow$ y=-2
So the first coordinate is (0,-2).
Now let us assume x=2, now by putting the value of x in equation(2), we get,
   2-y=2
$\Rightarrow$-y=2-2
$\Rightarrow$-y=0
$\Rightarrow$y=0,
So another coordinate is (2,0).
Now we will place these points (0,-2) and (2,0) on a graph sheet and by joining those two points by a scale we will get our required graph of x-y=2.

(iii) Now for equation(iii) which is,
y=3x…………….equation(3)
Since this is also a linear equation, so, we have to find two points which satisfy y=3x.
Let x=0, then by putting the value of x in equation(3), we get,
y=$3\times 0$
$\Rightarrow$ y=0,
So, our first coordinate is (0,0).
Now again ,taking x=1, we get,
y=$3\times 1$
$\Rightarrow$y=3,
So, we get another coordinate (1,3).
Now we will place these points (0,0) and (1,3) on a graph sheet and by joining those two points by a scale we will get our required graph of y=3x.

(iv) Now the last equation,
3=2x+y, which can be also arrange as,
2x+y=3……………...equation(4)
Now for finding the coordinates, let us assume that the value of x is 0, i.e, x=0, so by putting the value of x in equation(4), we get,
   0+y=3
$\Rightarrow$y=3,
 So our first coordinate is (0,3).
Now let another value of x is 1, so by putting in equation(4), we get,
$2\times 1+y=3$
$\Rightarrow$2+y=3
$\Rightarrow$y=3-2
$\Rightarrow$y=1,
So we get another point (1,1).
Now we will place these points (0,3) and (1,1) on a graph sheet and by joining those two points by a scale we will get our required graph of 3=2x+y.

So, we plotted all of the linear equations on graph paper,
Note: while plotting any linear equation you have to keep in mind that we can plot any linear equation on graph if we know at least 2 points also you can take 3 points or 4 points but it will consume more time, Apart from that while finding any coordinate you can take any value of x and by putting that value in the given linear equation you will get the value of y.