Question

What is the equation, in point-slope form, of the line perpendicular to the given line and passing through the point (2,5)?

A. y+5=x+2
B.y−2=x−5
C. y−5=−(x−2)
D. y+2=−(x+5)

Answer 1

The equation of the line perpendicular to the given line and passing through the point (2,5) is y - 5 = -(x - 2).

Step-by-step explanation:

To find the equation of a line perpendicular to a given line and passing through a specific point, we use the fact that the slopes of perpendicular lines are negative reciprocals of each other.

The given line has the equation y = mx + b, where m is the slope.

To find the slope of the perpendicular line, we take the negative reciprocal of m. Therefore, the equation of the line perpendicular to the given line and passing through the point (2,5) would be y - 5 = -(x - 2).