SOLUTION: Which statement is true of the given lines? Line a: -2x+y=4 Line b: 2x+5y=2 Line c: x+2y=4 a) Lines a and b are parallel. b) Lines a and c are parallel. c) Lines a and

Question 174231: Which statement is true of the given lines?
Line a: -2x+y=4 Line b: 2x+5y=2 Line c: x+2y=4
a) Lines a and b are parallel.
b) Lines a and c are parallel.
c) Lines a and b are perpendicular.
d) Lines a and c are perpendicular.
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
Rewriting each of the given equation into the "point-slope" form of
y = mx + b
.
Line a: -2x+y=4
y = 2x+4
.
Line b: 2x+5y=2
5y = -2x+2
y = (-2/5)x + 2/5
.
Line c: x+2y=4
2y = -x + 4
y = (-1/2)x + 2
.
Since NO two lines have the same slope -- no lines are parallel.
Now, if two lines are "negative reciprocals" then they are perpendicular.
Slope of line a: 2
Slope of line c: -1/2
They are "negative reciprocals" --
that is, if you multiply the two slopes you'll get -1
.
Answer would be -- d) Lines a and c are perpendicular.
RELATED QUESTIONS
Which describes the lines represented by these equations? y=1/2x-4 2y=x+2 A.... (answered by stanbon)

Which of the following is a line parallel to y = �x + 4? @ The slopes of parallel lines... (answered by checkley77)

which system has no solution? (a) lines 1 and 2 (b) lines 1 and 3 (c) lines 1 and 4 (d)... (answered by stanbon)

Ian graphs these equations and finds the lines intersect at a single point (-2, -0.5)... (answered by MathLover1)

State whether the statement is TRUE or FALSE. (a) y = 3x � 1 and y = 2x �1 are... (answered by ilana)

Which of the following statements are true ? a. the lines y = 2x - 5, y = ax... (answered by Alan3354)

Determine which of the following lines, if any, are perpendicular or parallel Line A:... (answered by ewatrrr)

Determine which lines are parallel to y=-3/2x+5. A.3x+2y=7 B. 3x-2y=4 C.3x+2y=5 D.The (answered by checkley71)

Considering the linear equations 1) (y )/2+3x-10=(x+y)/2 2) 3x/4+4=2y/3+2 a) What is... (answered by Alan3354,ikleyn)