Question 1: Draw the graph of each of the following linear equations:

(i) (i) (iii) (iv) (v)

(vi) (vii) (viii) (ix) (x)

(xi) (xii) (xiii) (xiv)

(xv) (xvi) (xvii)

(xviii) (xix) (xx)

Answer:

i) to viii)

ix) to xii)

xiii) to xvi)

xvii) to xx)

Question 2: Find the slope and y-intercept of the lines represented by each of the following equations: (i) (ii) (iii) (iv) (v)

Answer:

For finding the slope and y-intercept, convert the equation into the form

i)

and

(ii)

and

(iii)

and

(iv)

and

(v) $

and

Question 3: Draw the graph of the line represented by the equation . Also, find the coordinates of the points where the line meets with the coordinate axes.

Answer:

To draw the line

x | 0 | -2 |

y | 3 | 0 |

Question 4: Draw the graphs of the lines represented by each of the following equations: , Find the coordinates of the vertices of the triangle formed by the two lines and the y-axis.

Answer:

To draw the line $latex

x | 0 | 6 |

y | 4 | 0 |

To draw the line $latex

x | 0 | 1 |

y | -1 | 0 |

Vertices of the triangle are

Question 5: Draw the graphs of the following pairs of lines on the same graph paper and find their points of intersection. Are these lines perpendicular to each other? (i) , (ii) ,

Answer:

i)

To draw the line

x | 0 | -4 |

y | 4 | 0 |

To draw the line

x | 0 | 6 |

y | 6 | 0 |

Intersection is . They are perpendicular (from the graph we can see that). Also the slope of the first line is while the slope of the second line is . We know if the product of the two slopes is (which is the case here) the lines are perpendicular.

ii)

To draw the line

x | 0 | 6 |

y | 3 | 0 |

To draw the line

x | 0 | 4 |

y | 8 | 0 |

Intersection is . They are perpendicular (from the graph we can see that). Also the slope of the first line is while the slope of the second line is . We know if the product of the two slopes is (which is the case here) the lines are perpendicular.

Question 6: Draw the graph of the following pairs of lines on the same graph paper and hence check whether they are parallel or not:

(i) , (ii) , (iii) ,

Answer:

(i) ,

To draw the line

x | 0 | -(2/3) |

y | 2 | 0 |

To draw the line

x | 0 | (4/3) |

y | -4 | 0 |

The lines on the graph are parallel. Slope of first line is while the slow of the second line is also . This also proves that the lines are parallel as the slopes of the lines are equal.

(ii) ,

To draw the line

x | 0 | 2.5 |

y | 5 | 0 |

To draw the line

x | 0 | -7 |

y | 3.5 | 0 |

The lines on the graph are not parallel. Slope of first line is while the slow of the second line is also . This also proves that the lines are parallel as the slopes of the lines are not equal.

(iii) ,

To draw the line

x | 0 | (8/3) |

y | 4 | 0 |

To draw the line

x | 0 | -4 |

y | -6 | 0 |

The lines on the graph are parallel. Slope of first line is while the slow of the second line is also . This also proves that the lines are parallel as the slopes of the lines are equal.