What is an equation of the line that passes through the point (6,7) and is parallel to the line 2x-3y=92x−3y=9?

The equation of the line passing through the point (6, 7) parallel to the line is y = 2/3x + 3

The equation in slope - intercept form :

2x - 3y = 9

-3y = 9 - 2x

Divide both sides by - 3

y = - 3 + 2/3x

Using the points (6, 7)

7 = c + 2/3(6)

7 = c + 12/3

7 = c + 4

c = 7 - 4 = 3

c = 3

The equation of the parallel line is thus :

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Step-by-step explanation:

y=m₁x+b₁   ║   y=m₂x+b₂   ⇔    m₁ = m₂

{Two lines are parallel if  their slopes are equal}

Changing to slope-intercept form:

2x - 3y = 9         {subtract 2x from both sides}

-3y = -2x + 9        {divide both sides by (-3)}

y = ²/₃x - 3     ⇒    m₁=²/₃   ⇒   m₂=²/₃

The line y=²/₃x+b passes through point (6, 7) so the equation:

7 = ²/₃×6 + b  is true

7 = 4 + b

b = 3

Therefore equation in  slope-intercept form:

                                                     y = ²/₃x + 3

hi there!

first we need to find out how much they are adding to each number to make the next number.

ex: 4 + 4 = 8, 8 + 8 = 16, and so on.

so continuing with 32,

32 + 32 = 64

64 + 64 = 128

128 + 128 = 256

256 + 256 = 512

4, 8, 16, 32, 64, 128, 256, 512

the 8th term of the sequence will be 512

hope this ! ~

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