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given: equation of line y = 2x + 1, P (5, 4)
to find: equation of line parallel to the given line and passing through (5, 4)
slope of the given equation y = 2x + 1
m₁= 2 [ y = mx + c ]
as the two lines are parallel, then their slopes have to be equal.
therefore m₁ = m₂ = 2
equation of the line with m₂ = 2 and passing through (5, 4) is given by the following equation
y - y₁ = m (x - x₁)
=> y₁ = 4 x₁ = 5
=> y - 4 = 2 (x - 5)
=> y - 4 = 2x - 10
=> y - 2x - 4 + 10 = 0
=> y - 2x + 6 = 0
=> 2x - y - 6 = 0 [ multiply both sides with -1 ]
OR
=> y = 2x - 6
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