**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.

- Construct a linear equation in two variables.
- Let the number of pencils be xand number of pens be y.
- According to the given situation, 60 = 2x + 4y.
- Now we have to represent this situation on the graph paper.
- 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 - Take a graph paper and a cartesian system is drawn, i.e., x-axis and y-axis are drawn.
- 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).
- On joining the points A, B, C and D we get a straight line.

**Observation**

- We get a straight line, which represents the linear equation [fig. (i)].
- 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 ?

**Answer:**

Infinitely many solutions.

**Question 2.**

How many solutions will you obtained for 2x + 5 = 3 ?

**Answer:**

One solution.

**Question 3.**

Write solution of 6x+ 5 = 1.

**Answer:**

\(-\frac { 2 }{ 3 }\)

**Question 4.**

If x = 5, does the equation x + 5 = 10 verify ?

**Answer:**

Yes.

**Question 5.**

Write the solution for x= 1 in 2x+ y = 4.

**Answer:**

(1,2).

**Question 6.**

Write the geometric representation of y = 3 as an equation in one variable.

**Answer:**

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.

**Answer:**

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.

**Answer:**

(0,0) and (4,1).

**Question 9.**

Check whether the point (-3, -2) lies on the line -2x + y = 7.

**Answer:**

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

**Answer**

- (i)
- (i)
- (iii)
- (i)
- (i)
- (i)
- (iii)
- (iv)
- (ii)
- (iii)

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