## CBSE Class 9 Maths Lab Manual – Graph of Linear Equation

Objective
To obtain a linear equation and draw a graph which represents the linear equation.

Prerequisite Knowledge
Concept of linear equation.
To represent the co-ordinates on cartesian plane.

Materials Required
Graph paper, pens, pencil, eraser, ruler.

Procedure
Let us consider a situation. Suppose you have 60 rupees to spend. You went to a stationery shop to buy some pencils and some pens. Cost of 1 pencil is Rs. 2 and the cost of 1 pen is Rs. 4. Find the number of pencils and pens bought by you from the shop.

1. Construct a linear equation in two variables.
2. Let the number of pencils be xand number of pens be y.
3. According to the given situation, 60 = 2x + 4y.
4. Now we have to represent this situation on the graph paper.
5. By taking different values of x we get different values of y. Put different values of x given in table to get corresponding values y as shown.
 x 0 2 4 6 y 15 14 13 12
6. Take a graph paper and a cartesian system is drawn, i.e., x-axis and y-axis are drawn.
7. Plot the coordinates from the above table on the graph and name them as A(0,15), B(2,14), C(4,13), D(6,12).
8. On joining the points A, B, C and D we get a straight line. Observation

1. We get a straight line, which represents the linear equation [fig. (i)].
2. On the line there are infinitely many coordinates. But, according to the situation we have taken those points or coordinates which are natural numbers.

Result
We observed that for the given equation, we get a straight line on the graph paper which cuts the x-axis and y-axis.

Learning Outcome
We learnt that for any one degree equation whether in one variable or two variables, yye will get a straight line on the graph papers. For x = a, line is parallel to y-axis at a distance of a unit from origin. For y = b, line will be parallel to x-axis at a distance of b unit from origin.

Activity Time
For the other daily life situations students can draw linear equation on the graph.
e.g. 1. x=2y (cost of one apple is equal to cost of two oranges).
2. x + y = 7 (sum of number of pencils and erasers is 7).

Viva Voce

Question 1.
How many solutions will you obtained for x + y = 1 ?
Infinitely many solutions.

Question 2.
How many solutions will you obtained for 2x + 5 = 3 ?
One solution.

Question 3.
Write solution of 6x+ 5 = 1.
$$-\frac { 2 }{ 3 }$$

Question 4.
If x = 5, does the equation x + 5 = 10 verify ?
Yes.

Question 5.
Write the solution for x= 1 in 2x+ y = 4.
(1,2).

Question 6.
Write the geometric representation of y = 3 as an equation in one variable.
The graph is a line parallel to x-axis at a distance of 3 from origin.

Question 7.
The cost of a ribbon is twice the cost of a hair pin. Write this statement in two variables in linear equation.
x = 2y, where x is the cost of a ribbon and y is the cost of a hairpin.

Question 8.
Write any two solutions of x = 4y.
(0,0) and (4,1).

Question 9.
Check whether the point (-3, -2) lies on the line -2x + y = 7.
No, (-3, -2) does not lie on the given line.

Multiple Choice Questions

Question 1.
Find k, if y = 1, x = 2 is a solution of the equation 2x + 3y = k:
(i) 7
(ii) 5
(iii) 6
(iv) none of these

Question 2.
Is x + $$\frac { 1 }{ x }$$ = 4, a linear equation ?
(i) no
(ii) yes
(iii) cubic equation
(iv) none of these

Question 3.
Write the degree of 7x – 1=0:
(i) 0
(ii) 2
(iii) 1
(iv) none of these

Question 4.
Write the degree of 2x + 3y = 5:
(i) 1
(ii) 2
(iii) 0
(iv) none of these

Question 5.
Write whether the given equation is linear or not. x(x + 5) = -x(3 – x) + 7.
(i) yes
(ii) no
(iii) can’t say
(iv) none of these

Question 6.
In a five day international cricket match between India and Pakistan played in Lahore two Indian batsmen together scored 347 runs. Express this situation in the form of an equation:
(i) x + y = 347
(ii) x – y = 347
(iii) xy = 347
(iv) none of these

Question 7.
How many solutions are possible for the equation y = 3x + 5 ?
(i) one solution
(ii) two solutions
(iii) infinite solutions
(iv) none of these

Question 8.
Express x in terms of y. Given $$\frac { x }{ 3 }$$ +2y = 5.
(i) x = 3(2y – 5)
(ii) x = $$\frac { 2y+5 }{ 3 }$$
(iii) x = 15 – 2y
(iv) none of these

Question 9.
For what value of p, the point (p, 4) lies on the line 3x + y =10?
(i) 4
(ii) 2
(iii) 6
(iv) none of these

Question 10.
For what value of x, the expressions 2x – 20 and 48 – 2x are equal ?
(i) 40
(ii) 18
(iii) 17
(iv) none of these