Math help!?

Question

Use the slope-intercept form of a line to determine the relationship between the lines determined by these two equations:3x + 6y = 8
y = 2x - 8
1.)parallel
2.)perpendicular
3.)neither parallel nor perpendicular

Answer 1

3x + 6y = 8
y = 2x - 8

Your first step is to put both of these in the form y = mx + b (also known as slope-intercept form). Fortunately for us, the second equation's already in that form. The first equation is not.

3x + 6y = 8
6y = -3x + 8
y = (-3/6)x + (8/6)
y = (-1/2)x + (4/3)

So our two lines are

y = (-1/2)x + 4/3
y = 2x - 8

Comparing their slopes, which I'll call m1 for the first line and m2 for the second line,

m1 = (-1/2)
m2 = 2

They are parallel if they are the same.
They are perpendicular if the negative reciprocal of one of them is the other. In algegraic terms, if you multiply them together and you get (-1), then they are the negative reciprocal of each other.

They are neither in all other cases.

Since m1 = 2 and m2 = -1/2, multiplied together they give (-1), so they are perpendicular.

Answer 2

1) 6y=-3x + 8

y = -1/2 (x + 8/3)

2) y = 2 (x+4)

The other equation is already in slope intercept form. So the slopes inverse therefore the equations are perpendicular.

Answer 3

y = mx+b

solve for y: 3x+6y = 8
6y= -3x+8
y = -3/6 x + 8/6
y = -1/2 x + 4/3

The answer is perpendicular because the slope is the negative inverse. The slope in y=2x+8 is 2 and the slope in 3x+6y=8 is -1/2. The negative inverse of 2 is -1/2

Answer 4

2

Answer 5

Convert the first equation to:
y = (-1/2)x + 4/3
Now we see that its slope is -1/2.

The other equation has a slope of 2.

If the slopes were equal, the 2 lines would be parallel.

Instead, their product is -1. That means that the 2 lines are perpendicular (answer 2).

If their slopes had any other relationship (other than equal, or having a product of -1), they would be neither parallel nor perpendicular.

Answer 6

1. put both equations into y=mX+b form
y=2X-8 is correct
3X+6y=8 isn't so subtract 3X from both sides. then divide both sides by 6 so that it looks like y= -1/2X+8

2. compare the lines. they are perpendicular if they are opposite signs (-or+) AND reciprocals (EX: 6/5 and -5/6)
they are parallel if they have the same slope

ANSWER: 2

Answer 7

set up each equation in y=mx + b form..and figure out what each equations slope is from that (slope being the "m" in the equation)..they are parallel if they both have the same slope..they are perpendicular if they are the negative inverse of each other (ie. 2 and -1/2)..if neither than u choose choice 3..good luck!

Answer 8

3x + 6y = 8
6y=8-3x
y=4/3-1/2x
the lines are perpendicular if m1m2=-1
and fr the eqns,
2*(-1/2)=-1
hencce they are perpendicular

Answer 9

first:
3x+6y=8
6y = -3x+8
y = -1/2x + 2/3
Second:
y = 2x -8
Lines are perp because slopes are neg recips