Mathematics
Find the equation of a line:
(i) Whose slope is 4 and which passes through the point (3, 7)
(ii) Whose slope is –3 and which passes through the point (–2, 3)
Straight Line Eq
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Answer
(i) By point-slope form,
Equation of line : y - y1 = m(x - x1)
Substituting values we get,
⇒ y - 7 = 4(x - 3)
⇒ y - 7 = 4x - 12
⇒ y = 4x - 12 + 7
⇒ y = 4x - 5
⇒ 4x - y = 5.
Hence, equation of the line is 4x - y = 5.
(ii) By point-slope form,
Equation of line : y - y1 = m(x - x1)
Substituting values we get,
⇒ y - 3 = -3(x - (-2))
⇒ y - 3 = -3(x + 2)
⇒ y - 3 = -3x - 6
⇒ y = -3x - 6 + 3
⇒ y = -3x - 3
⇒ 3x + y + 3 = 0
Hence, equation of the line is 3x + y + 3 = 0.
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