Are the following lines parallel, perpendicular, or neither?
L1 with equation x – 4y = 12
L2 with equation 4x + y = 4
2006-11-24 10:27:14 · 4 answers · asked by jason wright 1 in Education & Reference ➔ Homework Help
First, put both equations into slope-intercept form (y = mx + b).
L1:
x - 4y = 12
x - 12 = 4y
y = (1/4)x - 3
L2:
4x + y = 4
y = -4x + 4
When two lines are parallel, they will have the same slope. When two lines are perpendicular, the slopes will be the opposite reciprocals of each other.
-4 and 1/4 are the opposite reciprocals of each other. Therefore, the two lines are perpendicular.
2006-11-24 10:45:14 · answer #1 · answered by Anonymous · 0⤊ 0⤋
The lines are perpendicular. Let's write each in the form
y = mx + b and compare slopes.
L1: y = x/4 - 3
L2: y = -4x + 4.
The slope of L1 is 1/4 and the slope of L2 is -4. Since
the product of these 2 numbers is -1, the lines are
perpendicular.
2006-11-24 18:42:58 · answer #2 · answered by steiner1745 7 · 0⤊ 0⤋
You have to put the equations into slope-intercept form first.
Line 1:
x – 4y = 12
-x . . . . . .-x
- 4y = -x + 12
------------------
. . . - 4
y = 1/4x + 12
Line 2:
4x + y = 4
-4x . . . . -4x
y = -4x + 4
Since -4 times 1/4 equals -1, your two lines are perpendiular.
2006-11-24 18:50:45 · answer #3 · answered by I'm a morning person. 3 · 0⤊ 0⤋
perpendicular
L1= y= -3-x
L2= y= 4-4x
2006-11-24 18:42:18 · answer #4 · answered by Anonymous · 0⤊ 0⤋