Are the following lines parallel, perpendicular, or neither?

Question

(L1with equation x-2y=10) and (L2 with equation 2X+Y=2)
Please show work - this is really hard!

Answer 1

alright..parallel lines have same gradient and perpendicular lines have gradients that multiply together to get -1 (e.g 2 and -1/2).

eqn 1: x-2y=10, -2y= -x+10, so y= (1/2)x -10, therefore grad is 1/2
eqn 2: 2x+y=2, y= -2x+2, so grad is -2.

Thus, the 2 eqns are not parallel to each other. Instead they are perpendicular lines.

Answer 2

L1: x-2y = 10
Rewrite in form y = mx + b to get the gradient (m):
2y = x - 10
y = (1/2) x - 5.
So the gradient of L1 is 1/2.

L2: 2x + y = 2
so y = 2 - 2x
so the gradient of L2 is -2.

Lines are parallel if they have the same gradient and perpendicular if the gradients multiply to -1. Here (1/2) . (-2) = -1 so L1 and L2 are perpendicular.

Answer 3

If you put the equations into y='s form then you can graph them alot easier. x-2y=10 is y=(-1/2)x+10 and 2x+y=2 is y=(-2)x+2. Seeing how they have different slopes, they are not parallel. To be perpendicular, the equations would have to be reciporicals, which they are, making them perpindicular.

Answer 4

rewrite equation of lines as

L1 => y = (1/2)*x - (10/2)
L2 => y = -2x + 2

slope of L1 = 1/2, slope of L2 = -2

product of slopes = -1/2 * 2 = -1 ; therefore lines are perpendicular

Answer 5

You have to get the equations into y=mx+b form to determine the slope, so for line one:

x-2y=10
x=10+2y
2y=x-10
y=(1/2)x-5
so the slope for this one is 1/2

The second:

2x+y=2
y=2-2x
y=-2x+2
so the slope is -2

By defeinition, perpendicular lines have opposite-reciprocal slopes. 1/2 is the opposite reciprocal of -2, so the lines are in fact perpendicular.

Answer 6

for L1
x - 2y = 10
-2y = -x + 10
y = 1/2 x + 5

the slope of this function is 1/2

for L2
2x+y = 2
y = -2x + 2

the slope of this function is -2


If the multiplication of the two slope is -1, the two lines are perpendicular

slope 1 x slope 2 = 1/2 x -2 = -1

thus, those lines are perpendicular.

Answer 7

get y on one side for both equations, and then find the slope for each.
y=(1/2x)-5
y=-2x+2
the slope for each are
1/2
-2
slope is the number infront of the x
if the slopes are same like 2 and 2, then it is parallel
if the slopes are different like 1 and 3, it is neither
if the slopes are opposite like 1/3 and -3, (switch the denominator and numerator, then change the sign to +/-) it is perpendicular
perpendicular-answer

Answer 8

In slope intercept form:
L1 : y = (x/2) -5
L2 : y = -2x +2

They are perpendicular because one of the slopes is the negative reciprocal of the other. If the slopes were the same, they would be parallel.

Answer 9

x-2y = 10
0.5x-y = 5
-y = 5-0.5x
y = -0.5x+5

2x+y=2
y = 2-2x
y = -2x + 2

Using y = mx+c (where m = the gradient of the line):

Line one: m = -0.5
Line two: m = -2

Comparing gradients they are obviously not parallel. For the lines to be perpendicular, one gradient would have to be positive, whilst the second would have to be negative.

Therefore, the lines are NEITHER parallel or perpendicular.

Answer 10

find out the slopes of the lines
L1 --- x - 2y = 10
2y = x - 10
y = 1/2 x - 5,
slope of L1 = 1/2

L2 -------- 2x + y = 2
y = -2x +2
slope of L2 = -2
slopes of L1and L2 are not equal, so there are not parallel
product of slopes = 1/2 * (-2) = -1
so the given lines are perpendicular since product of slopes is -1.