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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

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 = b = – 2a = = -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 |

(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

X | l | 4 |

y | 1 | -3 |

(x,y) | (1 × 1) | (4-3) |

When x=1, =

When x = 4,

X | -1 | 5 |

y | 2.5 | -2 . |

(x,y) | (-1,2.5) | (5-2) |