Question

check whether the lines x + y = 1 and 2x + y = x + 2 are either parallel or

perpendicular.​

Answer 1

SOLUTION

TO CHECK

The lines x + y = 1 and 2x + y = x + 2 are either parallel or perpendicular.

CONCEPT TO BE IMPLEMENTED

Two given lines are

• Parallel if their slopes are equal

• Perpendicular if product of their slopes = - 1

EVALUATION

Here the given equation of the lines are

x + y = 1 and 2x + y = x + 2

So the equation of the first line

$\sf{x + y = 1}$

$\sf{ \implies \: y = - x + 1}$

So slope of the first line = - 1

The equation of the second line is

$\sf{2x + y = x + 2}$

$\sf{ \implies \: y = - x + 2}$

So the slope of the second line = - 1

Since the slopes of given two lines are equal

Hence the given two lines are parallel

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