The table below represents the distance of a car from its destination as a function of time:
(I'll post the table right now, also person who helps gets a medal, fan, and testimony)
Part A: What is the y-intercept of the function and what does this tell you about the car?
Part B: Calculate the average rate of change of the function represented by the table between x = 1 to x = 3 and what does the average rate represent?
Part C: What would be the domain of this function if the car traveled the same rate until it reached its destination?

- anonymous

- jamiebookeater

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- anonymous

Time (Hour) x Distance (Miles) y
0 900
1 850
2 800
3 750

- anonymous

I have absolutly no clear what I am doing but I have only 5 minutes to get the answer. :O

- nincompoop

can you try to graph it first? this is an important skill to hone and then we can try to solve for other things analytically and graphically

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- anonymous

I would except I don't have graph paper or anything like it

- nincompoop

oh this is a study site, not answer my homework site

- anonymous

I understand that completely

- nincompoop

try to solve for the slope from the start of the time and distance (initial) and end time and distance (final)

- anonymous

Never mind I ran out of time, thanks anyway :). I'll still fan, medal, and write a testimony about you though.

- nincompoop

time (x) distance (y)
x initial (x1) y initial (y1)
x.. y..
x.. y..
x.. y...
x final (x2) y final (y2)

- Teddyiswatshecallsme

Part A is just talking about what is it the Y-intercept of the function, in other words, which column which is the y and what does it say about the equation?

- anonymous

ok

- nincompoop

once you figure out the slope, then you can use the slope-intercept form \((y-y_1) = m \times (x-x_1) \) solve for y and whatever your constant is the y-intercept

- anonymous

I am still confsued about part b though

- nincompoop

average rate of change is just your slope :)

- Teddyiswatshecallsme

Nin that's point slope form.

- Teddyiswatshecallsme

Not Slope Intercept.

- anonymous

Sorry guys I am just confused because I am a 7th grader and this is way beyand me.

- Teddyiswatshecallsme

Slope Intercept: y = mx + b

- Teddyiswatshecallsme

Hmm, then why do you have this homework?

- nincompoop

point-slope form and slope-intercept form are related. you cannot arrive into the latter without solving the former in this scenario

- anonymous

I have this homeowkr because I am taking this advanced course

- Teddyiswatshecallsme

Ahhh alright.

- nincompoop

try doing what I have been telling you and then we will go through them individually

- anonymous

Ok umm, hang on

- nincompoop

I will give you the graphical and analytical point of view of the words such as intercepts

- nincompoop

teaching you the concepts will help you solve future problems compare to telling you how to solve this.

- nincompoop

at no extra cost :)

- nincompoop

just pay me with your attention (time)

- anonymous

OK so what do I do for the first step? to solve part b?

- nincompoop

so average rate of change or any rate of change pertains to the slope, m

- anonymous

Is there a formula for that?

- Teddyiswatshecallsme

Yes.

- nincompoop

have you got an idea what slope is yet?

- anonymous

m = y1- y2 / x1 - x2? is that right?

- nincompoop

correct

- anonymous

Yes!

- nincompoop

now that is analytically looking at things, but what if you are not provided the x's and y's and you have to figure them yourself?

- nincompoop

bear with me, I will draw some things for you to look at

- anonymous

Yes, I was just about to say dosn't slope only work for points? (ex. (3, 5) or (-2, 7))

- nincompoop

it does and then we can use that same knowledge to solve any related-rate problem

- nincompoop

|dw:1435975261422:dw|

- nincompoop

we can say that your average rate of change (how much you're traveling at every moment in time) or simply your speed is going to be \(\large s = \frac{final~distance - initial~distance}{final ~time - initial~ time} \)

- anonymous

I understand this now thanks so much can you help with one more?

- anonymous

I got the answer right!

- nincompoop

let us not try to skip because it will expand and be more complicated from this

- anonymous

Yes, I understood this and I wrote down my answer and got it right, I just need help with one more thing.

- anonymous

Explain how the Quotient of Powers was used to simplify this expression: \[2^{5}/8 = 22\]
By finding the quotient of the bases to be 1/4 and cancelling common factors
By finding the quotient of the bases to be 1/4 and simplifying the expression
By simplifying 8 to 23 to make both powers base two and subtracting the exponents
By simplifying 8 to 23 to make both powers base two and adding the exponents

- nincompoop

now if we represent first drawing into graph, this is where the x's and y's appear
|dw:1435975525773:dw|

- nincompoop

thank you for your time. I do not like being rushed when I am trying to provide critical concepts.

- nincompoop

|dw:1435975838805:dw|

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