Write the equation of a line that passes through the point (1, 2) and is perpendicular to the line y = x + 5.

Solution:

The product of the slopes of two perpendicular lines is always -1.

Let the slope of the required line be m. The slope of given line y = x + 5 is 1.

Since the required line is perpendicular to the line y = x + 5, m × 1 = -1

⇒ m = -1

Also, the required line passes through (1,2).

Using the point slope form of the equation, we get:

 (y - y₁) = m (x - x₁)

⇒ (y - 2) = -1(x - 1)

⇒ y -2 = -x + 1

⇒ y = -x + 3

Thus, the equation of a line that passes through the point (1, 2) and is perpendicular to the line y = x + 5 is y = -x + 3.

Write the equation of a line that passes through the point (1, 2) and is perpendicular to the line y = x + 5

Summary:

The equation of a line that passes through the point (1, 2) and is perpendicular to the line y = x + 5 is y = -x + 3.