QQuestion
(a) If the lines kx − y + 4 = 0 and 2y = 6x + 7 are perpendicular to each other, find the value of k.
(b) Find the equation of a line parallel to 2y = 6x + 7 and passing through (−1, 1).
✓Answer
(a) For the first line:
kx − y + 4 = 0
⇒ y = kx + 4
Therefore, its slope m₁ = k.
For the second line:
2y = 6x + 7
⇒ y = 3x + 7/2
Therefore, its slope m₂ = 3.
For perpendicular lines:
m₁m₂ = −1
⇒ k × 3 = −1
⇒ k = −1/3
(b) A line parallel to 2y = 6x + 7 has slope 3.
Using the point-slope form through (−1, 1):
y − 1 = 3[x − (−1)]
⇒ y − 1 = 3(x + 1)
⇒ y − 1 = 3x + 3
⇒ y = 3x + 4
Therefore, k = −1/3 and the required parallel line is y = 3x + 4.
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