Which equation represents the line that
passes through and is perpendicular
to the line ?
(A)
(B)
©
(D)

To find the equation of the line that passes through the point and is perpendicular to the given line , we need to determine the slope of the new line. The slope of the given line is 2, so the slope of the perpendicular line will be the negative reciprocal, which is .

Using the point-slope form of a line, , where is the point and is the slope, we plug in and :

This aligns with option (B) .

So, the correct answer is (B) .

In terms of real-world applications, mastering concepts such as slopes and perpendicular lines is vital for fields like architecture and engineering. These professionals often need to design structures with specific angles and inclines, ensuring stability and aesthetics.

Additionally, when solving equations of lines, a common mistake is to incorrectly determine the negative reciprocal of a slope. Remember, it’s easy to miscalculate under pressure, so double-check both your slope and arithmetic to ensure accuracy!