The equation of line XY is (y − 3) = (x − 4). What is the slope of a line perpendicular to XY?

Perpendicular lines are those lines that intersect at 90 degrees. Let's see how we can find the slope of a line perpendicular to another line.

Answer: The slope of the line perpendicular to XY is -1.

Let's understand the problem in detail.

Explanation:

To find the slope of a line perpendicular to another line we will use the formula below

m\(_1\)m\(_2\) = -1, where m\(_1\) is the slope of the first line and m\(_2\) is the slope of the second line.

Here, the line given is (y − 3) = (x − 4).

If we write it as y = mx + c, we get y = x - 1.

Hence, the slope of the line is 1. Let it be m₁ = 1

Now, to find the slope of the perpendicular line (m\(_2\)), we use m\(_1\)m\(_2\) = -1,

Thus, we get m\(_2\) = -1.

Hence, the slope of the line perpendicular to XY is -1.