Are these lines parallel, perpendicular or neither and why?

Question

2x - 4y = 16 OR (y = -1/2x + 4)

and

6x + 3y = -4 OR (y = -1/2x - 4/3)

Answer 1

The lines are parallel as their slopes (m = -1/2) are the same. One line intersects the y-axis at +4, the other at -4/3.

Answer 2

those are not the simplified forms of the lines in slope-intercept form.

2x - 4y = 16

x - 2y = 8

  x - 8 = 2y

(1/2)x  - 4 = y

6x + 3y = -4

6x + 4 = -3y

-2x - 4/3 = y

the two lines are perpendicular.  The slopes of the lines satisfy m1*m2 = -1

(-2)(1/2) = -1

Answer 3

they are parallel because as you can see from the graphs that they do not intersect with eachother unlike a perpendicular graph.

Answer 4

When they are in y = mx + b form, it's easier...

y = (-1/2)x + 4

y = (-1/2)x - (4/3)

In both equations, the slope (m) is the same. So these lines are parallel.  Since the y-intercept (b) is different in each, they are NOT the same line.

Answer 5

2x-4y=16=>

4y=2x-16=>

y=(1/2)x-4----(1)

6x+3y=-4=>

3y=-6x-4=>

y=-2x-4/3-----(2)



The slope of (1) & (2) are

m1=1/2 & m2=-2

m1*m2=-1=>

the 2 lines are perpendicular

You need to do more fundamental exercises in algebra.

Answer 6

i. 2x - 4y = 16 =>

-4y = 16 - 2x

4y = 2x - 16

y = x/2 - 4

ii. 6x + 3y = -4 =>

3y = -6x - 4

y = -2x - 4/3

The slope of (i) is 1/2

The slope of (ii) is -2

Their product is -1, thus the lines are perpendicular.

Answer 7

Looking at y=-1/2x+4

slope is coefficient of x or -1/2 which is the slope

The other equation also has a coeficient = -1/2

Slopes are equal so lines are parallel.

Answer 8

They are parallel since they both have the same slope, -1/2. If you put a line in y=mx+b format, the 'm' is the slope.

Answer 9

They are parallel because they have the same slope, -1/2

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