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The two lines
y = m1x + c1 and y = m2x + c2
are parallel if their gradients are equal [i.e. m1 = m2]
are perpendicular if the product of their gradients is –1 [i.e. m1 × m2 = −1]
are coincident if and only if m1 = m2 and c1 = c2
(a) State, with reasons, if each of the following pair of lines are parallel, perpendicular or
coincident [Two lines are coincident if they lie on top of each other].
i. 2y = 6x − 4, 2 + y − 3x = 0
ii. x + y − 4 = 0, x + 2 = y
iii. 5y + 10x = 5, y + 2x = 2
iv. y = 2x + 1, y = 3x − 2
(b) How many solutions would each of the lines in (a) above have? None? One? Two? Infinite?
Give a reason in each case.?
In Mathematics
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Asked by kayla on 26th October, 2021
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