Determine which of the following lines are parallel or perpendicular?

Question

1. line a: -3x-12y=36 line b: x + 4y = 2 line c: y= 4x

2. Write an equation of the line that passes through ( 5,3) and is perpendicular the line y= -5x + 3

Answer 1

1.  Find the slope of each line by solving for y.

line a: y = (-1/4)x - 3 ______slope = -1/4

line b: y = (-1/4)x + 1/2____ slope = -1/4

line c: y = 4x____________slope = 4

Lines a and b are parallel because their slopes are equal.

Because (-1/4)(4) = 1, both lines a and b are perpendicular to line c.

2.  The slope of the line y = -5x + 3 is -5.

The slope of a perpendicular line will be the negative reciprocal of -5.  That means the slope will be 1/5.

The equation of a line is

y-y1 = m(x-x1), where m is the slope and (x1,y1) is a point on the line.  You know m = 1/5, and your point is (x1,y1) = (5,3).

Finish the problem by plugging those in.