Graphical Solution Of a Linear Equation
Linear equations in two variable of Class 9
(A) in order to draw the graph of a linear equation in one variable we may follow the following algorithm.
Step I :Obtain the linear equation.
Step II: If the equation is of the form ax = b, a ≠ o, then plot the point and one more point when α is any real number. If the equation is of the form ay = b, a ≠ 0, then plot the point and where β is any real number.
Step III: Joint the points plotted in step II to obtain the required line.

If eq. is in form ax = b then we get a line parallel to Yaxis and if eg. is in form ay = b then we get a line parallel to Xaxis. 
question . Draw the graph of
(i) 2x + 5 = 0 (ii) 3y  15 = 0
Solution: (i) Graph of 2x + 5 = 0
On simplifying it we get 2x = –5 ⇒ x = – 5/2
First we plot point A1 & then we plot any other point A2 on the graph paper, then we join these two points we get required line as shown in figure below.
(ii) Graph of 3y  15 = 0
On simplifying it we get 3u = 15 ⇒ y = 15/3 f = 5.
First we plot the point B1 (0, 5) & then we plot any other point B2 (3, 5) on the graph paper, then we join these two points we get required line m as shown in figure.
NOTE:
(A) A point which lies on the line is a solution of that equation. A point not lying on the line is not a solution of the equation.
(B) In order to draw the graph of a linear equation ax + by + c = 0 may follow the following algorithm.
Step I : Obtain the linear equation ax + by + c = 0.
Step II : Express y in terms of x i.e. y = or x in terms of y i.e. .
Step III : Put any two or three values for x or y and calculate the corresponding values of y or x respectively from the expression obtained in Step II. Let we get points as .
Step IV : Plot the points on graph paper.
Step V : Joint the pints marked in step IV to obtain. The line obtained is the graph of the equation ax +by + c = 0.
5. Draw the graph of the line x – 2y = 3, from the graph find the coordinate of the point when
(i) x = – 5 (ii) y = 0
Solution: Here given equation is x  2y = 3.
Solving it for y we get 2y = x  3 ⇒ y =
Let x = 0, then
x = 3, then y = = 0,
x =  2, then y = Hence we get
x 
0 
3 
2 
y 
 3/2 
0 
 5/2 
Clearly when x =  5 then y =  4 and when y = 0 then x = 3.
question . Draw the graphs of the lines represented by the equations x + y = 4 and 2x  y = 2 in the same graph. Also find the coordinate of the point where the two lines intersect.
Solution: Given equations are
x + y = 4 ......(i) & 2x  y = 2 ......(ii)
(i) We have y = 4  x
x 
0 
2 
4 
y 
4 
2 
0 
(ii) We have y = 2x – 2
x 
1 
0 
3 
y 
0 
–2 
4 
By drawing the lines on a graph paper, clearly we can say that P is the point of intersection where coordinates are x = 2, y = 2.