Write an equation of the line containing the given point and parallel to the given line. Let us consider that the given point is (1, 2) and the line is x + y = 1.
We will use the concept of straight lines in order to find the equation of the line.
Answer: y = - x + 3 is the equation of our required line.
Let us see how we will use the concept of straight lines in order to find the equation of the line.
For the line x + y = 1, this line can also be written as y = 1 - x.
Hence, the slope of the line y = 1 - x is -1. [Since, for y = mx + c, m is the slope]
Since our required line is parallel to the line x + y = 1, hence the slope of our required line is also -1. [Since, parallel lines have same slopes]
Now let us consider that our required line also passes through the point (x, y).
From the definition of slope we can also write,
(y - 2) / (x - 1) = -1 [The points are (1, 2) and (x, y)]
⇒ y - 2 = - x + 1
⇒ y = - x + 3