KSEEB Solutions for Class 8 Maths Chapter 14 Introduction of Graphs Ex 14.2

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Karnataka State Syllabus Class 8 Maths Chapter 14 Introduction of Graphs Ex 14.2

Question 1.
Draw the graphs of the following straight lines.
(i) y = 3 – x
(ii) y = x – 3
(iii) y = 3x – 2
(iv) y = 5 – 3x
(v) 4y = – x + 3
(vi) 3y = 4x + 1
(vii) x = 4
(vii) 3y = 1
Answer:
(i) y = 3 – x

x	0	1	2
y	3	2	1

When x = 0, y = 3 – 0 = (3)
When x = 1, y = 3 – 1 = (2)
When x = 2, y = 3 – 2 = (1)

(ii) y = x – 3

X	0	1	2
y	-3	-2	-1

When x = 0,                           y = 0 – 3 = (- 3)
When x = 1,                        y = 1 – 3 = (- 2)
Whenx = 2,                            y = 2 – 3 = (- 1)

(iii) y = 3x – 2

X	0	1	2
y	-2	1	4

When x = 0,                           y = 3(0) – 2 = (- 2)
When x = 1,                        y = 3(1) – 2 = (1)
Whenx = 2,                            y =3(2) – 2 = (4)

(iv) y = 5 – 3x

X	0	1	2
y	5	2	-1

When x = 0, y = 5 – 3(0) = 5
When x = 1, y = 5 – 3(1) = 2
Whenx = 2, y = 5 – 3(2) = 5 – 6 = – 1

(v) 4y = – x + 3

(vi) 3y = 4x + 1

X	-1	2	5	8
y	-1	3	7	11
(x,y)	(-1,0	(2,3)	(5,7)	(7,11)

(vii) x = 4

X	4	4	4	4
y	0	1	2	3
(x,y)	(4,0)	(4,0	(4,2)	(4,3)

(vii) 3y = 1

Question 2.
Draw the graph of $\frac{y}{x}=\frac{y+1}{x+2}$
Answer:
When x = 1

Question 3.
Determine the equation of the line in each of the following graphs

Answer:
(i) Let the equation be y = ax + b
We find that the lines passes through (2,0)
i. e., when x = 2, y = 0
∴ y = ax+b
0 = ax + b
0 = a(2) + b
0 = 2a + b
∴ b = – 2a
The line passes through (4,3) also
i. e., when x=4 , y = 3
∴ y = ax + b
3 = a(4) + b
3 = 4a + b
3 = 4a + (-2a)
3 = 4a = 2a
a = $\frac { 3 }{ 2 }$ b = – 2a = $-2 \cdot \frac{3}{2}$ = -3
y = ax + b y

The equation is 3x – 2y = 6

(ii) Let the equation be y = ax + b
we find that the line passes through (5, 0)
i.e., when x = 5, y = 0
∴ y=ax + b
0 = a(5) + b
0 = 5a + b
b = -5a
The line passes through (0 , 5)also
i.e.,when x = 0, y = 5
y = ax + b
5 = a(0) + b
5 = 0 + b
5 = 0 + (-5a)
5 = -5a
∴ a = $\frac { -5 }{ 5 }$
a = -1
b = -5a = -5(-l) = 5 b = 5
b = 5
y=ax + b
y = – 1 x + 5 y = – x+ 5 y + x = 5
The equation of the line of is y + x=6

Question 4.
A boat is moving in a river, downstream, whose stream has speed 8km/hr. the speed of the motor of the boat is 22km/hr. Draw the graph of the distance covered by the boat versus an hour.
Answer:
Speed of the boat down stream = 22 + 8 = 30 km/hr
y = 30x

Time	i	2	3	4	5
Distance	30	60	90	120	150
Distance	(1,30)	(2,60)	(3,90)	(4.120)	(5,150)

Question 5.
Find the point of intersection of the straight lines 3y + 4x = 7 and 4y + 3x = 7, by drawing their graphs and looking for the point where they meet.
Answer:
3y + 4x = 7
3y = 7 – 4x
$y-\frac{7-4 x}{3}$

X	l	4
y	1	-3
(x,y)	(1 × 1)	(4-3)

When x=1, $y-\frac{7-4 x}{3}$ = $\frac{7-4}{3}=\frac{3}{3}=1$
When x = 4,

X	-1	5
y	2.5	-2 .
(x,y)	(-1,2.5)	(5-2)