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Find the equation of the straight line which passes through the point of intersection of the straight lines x + y = 6 and x + 2y - 8 = 0 and is parallel to the straight line joining the points (3, 4) and (5, 6)

Find the equation of the straight line which passes through the point of intersection of the straight lines x + y = 6 and x + 2y - 8 = 0 and is parallel to the straight line joining the points (3, 4) and (5, 6) Correct Answer None of these

As per the given data,

x + y = 6            ….. (1)

x + 2y - 8 = 0     ….. (2)

From equation (1) and equation (2), we get

⇒ x = 4 and y = 2

∴ Point intersection of the lines x + y = 6 and x + 2y - 8 = 0 is (4, 2)

We know that,

Two point form of a line through the points (x1, y1) and (x2, y2) is (y - y1) = × (x - x1)

Equation of the line with points (3, 4) and (5, 6)

⇒ (y - 4) = × (x - 3)

⇒ (y - 4) = (x - 3)

⇒ x - y + 1 = 0

We know that,

Slope of line ax + by + c = 0 is –b/a

⇒ Slope of the line x - y + 1 = 0 is - (-1)/1 = 1

∴ Required line has a slope of 1 and passes through the point (4, 2)

We know that,

Point - slope form of a line through the point (x1, y1) and slope ‘m’ is (y - y1) = m(x - x1)

Line passing through (4, 2) and with slope 1 is

⇒ (y - 2) = 1 × (x - 4)

⇒ (y - 2) = x - 4

⇒ x - y - 2 = 0

∴ Required line is x - y - 2 = 0

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