The equations of three lines are given below.
line 1: 3y = -4x + 4
line 2: 6x + 8y = 6
line 3: y = - 4 / 3 x - 7
the fraction is negative
for each pair of lines, determine whether they are parallel, perpendicular, or neither.
line 1 and line 2: parallel, perpendicular, or neither
line 1 and line 3: parallel, perpendicular, or neither
line 2 and line 3: parallel, perpendicular, or neither

ANSWER

line 1 and line 2: neither

line 1 and line 3 : parallel

line 2 and line 3: neither

EXPLANATION

The equation of line 1 is

3y = -4x + 4

We rewrite in slope intercept form to get:

The slope is

The second line is:

6x + 8y = 6

We rewrite in slope intercept form to get,

The slope is

The third line is

line 1 and line 2: are neither parallel nor perpendicular because the two slope s are not the same and their product is not -1.

line 1 and line 3 are parallel because their slopes are the same

line 2 and line 3:are neither parallel nor perpendicular because the two slopes are not the same and their product is not -1.

1. sometimes

2.   never

3   .08c = 7.50+.05c   250 pages

step-by-step explanation:

1.   sometimes

the theoretical probability of rolling a 1 is 1/6.   perhaps you got really lucky and never rolled a 1   in those 60 times.   your experimental probability is 0.   or perhaps you rolled a 1   20 times.   your experimental probability is 20/60 is 1/3.     it really just depends on how you rolled in that experiment.

2.   never

the probability of the event occurring is 1.   that is being 100 % sure it will happen.   that is the maximum amount of confidence we have.

3.   no customer card cost:   .08 times number of pages

customer card cost:   7.50 + .05 times number of pages

we want to find when it costs the same amount, so we will set these equal

let c = number of pages

.08c = 7.50+.05c

subtract .05c from each side

.08c-.05c = 7.5+.05c-.05c

.03c=7.5

divide each side by .03

.03c/.03 = 7.5/03

c =250  

the cost is the same at 250 pages