Question

1) What is the equation of the line perpendicular to y = (1/2)x - 2 that

contains the point (2, 5)?
y-5= -2(x - 2)
y-5=-1/2(x - 2)
y-2=-2(x - 5)
y- 5 = 1/2(x - 2)

Answer 1

(a) y -5= -2(x -2)

Explanation:

You want the equation of the line perpendicular to y = (1/2)x - 2 that contains the point (2, 5).

Perpendicular lines

Perpendicular lines have slopes that are opposite reciprocals of one another. The slope of the given line is the x-coefficient: 1/2. Its opposite reciprocal is ...

-1/(1/2) = -2

Point-slope equation

The point-slope equation of a line is ...

y -k = m(x -h) . . . . . . . . line with slope m through point (h, k)

You want a line with slope -2 through point (2, 5), so its equation is ...

y -5 = -2(x -2)