# 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
(i) y = 3 – x

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

(ii) y = x – 3

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

(iii) y = 3x – 2

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

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

(vii) x = 4

(vii) 3y = 1

Question 2.
Draw the graph of yx=y+1x+2
When x = 1

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

(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 = 32 b = – 2a = −2⋅32 = -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(-1) = 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.
Speed of the boat downstream = 22 + 8 = 30 km/hr
y = 30x

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.
3y + 4x = 7
3y = 7 -4x
y−7−4×3

When x=1, y−7−4×3 = 7−43=33=1
When x = 4,

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