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.

Solution:

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

Hence, y = - x + 3 is the equation of our required line.

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.

Summary:

y = - x + 3 is the equation of our required line.