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Short Questions (Question 3, 4 & 5)

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Question 3:
The equation of the straight lines CD and EF are 5x + y – 4 = 0 and x 7 − y h = 1 . If CD and EF are parallel, find the value of h.

Solution:
Two parallel lines have same gradient.
 5x + y – 4 = 0  
 y = –5x + 4, mCD = –5

 For the straight line EF,
x 7 − y h = 1 m E F = − ( y -intercept x -intercept ) = − ( − h 7 ) = h 7 m C D = m E F − 5 = h 7 h = − 35




Question 4:
The straight line x 5 + y p = 1 has a y-intercept of 3 and is parallel to the straight line y + qx = 0. Determine the value of p and of q.

Solution:
Given y-intercept of the straight line  x 5 + y p = 1  is  3 , ∴ p = 3 Gradient of the straight line =  − 3 5 For another straight line  y + q x = 0 ,   y = − q x As two parallel lines have same gradient, − q = − 3 5 q = 3 5



Question 5:
The equations of two straight lines   y 7 + x 4 = 1 y = 4x + 21. Determine whether the lines are perpendicular to each other.

Solution:
For the straight line  y 7 + x 4 = 1 ,  gradient  = − 7 4 For the straight line  7 y = 4 x + 21 , y = 4 7 x + 3 ,  gradient  = 4 7 − 7 4 × 4 7 = − 1

Hence, the two straight lines are perpendicular to each other.