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Mathematics 13 Online
OpenStudy (horsegirl27):

Need help fast please! I will medal and fan please help me! Question below

OpenStudy (horsegirl27):

Sam rented a boat for 2 days for $225. He then rented the same boat for 5 days for a cost of $480. A: right it in standard form with y being the total cost and x being the number of days B: right it in function notation C;describe how you would graph it

OpenStudy (anonymous):

I... don't get it....

OpenStudy (horsegirl27):

It has a typo it should be write not right

OpenStudy (anonymous):

@iGreen

OpenStudy (anonymous):

Just message iGreen and he'll help. :P

OpenStudy (horsegirl27):

ok I did

OpenStudy (anonymous):

bahh, sorry this it tots off topic, but i seen horse and i love equestrians cuz im one XD just had to comment

OpenStudy (horsegirl27):

oh cool haha could you help as well?

OpenStudy (anonymous):

two days cost $225, should be $112.5 per day

OpenStudy (horsegirl27):

Help me please @satellite73 @iGreen @blurbendy

OpenStudy (horsegirl27):

@butterflydreamer Help!!

OpenStudy (horsegirl27):

@iGreen

OpenStudy (horsegirl27):

I need help with A B and C I don't understand them

OpenStudy (igreen):

First we find the slope..we are given two points: (2, 225) and (5, 480) Plug them into the slope formula: \(m = \dfrac{y_2-y_1}{x_2-x_1}\) \(m = \dfrac{480-225}{5-2}\) Can you simplify that? @horsegirl27

OpenStudy (horsegirl27):

Ok

OpenStudy (horsegirl27):

255/3

OpenStudy (horsegirl27):

85/1

OpenStudy (horsegirl27):

Is that right?

OpenStudy (horsegirl27):

@iGreen

OpenStudy (igreen):

Yes.

OpenStudy (igreen):

So the slope is 85.

OpenStudy (horsegirl27):

Ok. What's the next step?

OpenStudy (igreen):

So to figure out the equation we plug in the slope with one of the two points we have..let's take the first point, (2, 225) and we plug it into point-slope form. \(y - y_1 = m(x - x_1)\) Where \(y_1\) is the y-value of the point, \(x_1\) is the x-value of the point, and \(m\) is the slope. \(y - 225 = 85(x - 2)\) Distribute 85 into the parenthesis: \(y - 225 = 85x - 170\) Now add 225 to both sides, what do you get?

OpenStudy (horsegirl27):

y=85x+55

OpenStudy (horsegirl27):

Is that right @iGreen

OpenStudy (igreen):

Yep, you got it..so that's our equation.

OpenStudy (igreen):

Oh wait..it says in standard form..so we have to change it to: \(Ax + By = C\)

OpenStudy (horsegirl27):

We do need it that way also I think

OpenStudy (igreen):

\(y = 85x + 55\) Subtract 85x to both sides: \(85x - y = 55\)

OpenStudy (igreen):

There we go..

OpenStudy (horsegirl27):

So that is A?

OpenStudy (igreen):

Okay, for B, function notation is just solving for 'y' then replacing 'y' with 'f(x)'. We already had y = 85x + 55, so just replace 'y' with 'f(x)'.

OpenStudy (igreen):

Yes, that was A.

OpenStudy (horsegirl27):

Thanks so much!

OpenStudy (horsegirl27):

Now what is B? I forgot function notation lol

OpenStudy (igreen):

I just told you :P

OpenStudy (horsegirl27):

oh cool lol haha

OpenStudy (horsegirl27):

Now for C I need to describe what the graph would look like. I have to mention the y-intercept, labels, intervals...

OpenStudy (horsegirl27):

I need help with that.

OpenStudy (horsegirl27):

@iGreen

OpenStudy (igreen):

Okay, well the x-axis will be labeled 'days', and the y-axis will be labeled 'cost'. The y-intercept is given in our formula 'y = 85x + 55', which is 55. And the line would go through the two points (2, 225) and (5, 480).

OpenStudy (horsegirl27):

\(\\\bbox [10pt, #00ffab,border:5pt solid blue ]{\color{#872AF0}{\huge\cal ~\heartsuit Thanks!\heartsuit}}\)

OpenStudy (horsegirl27):

Thank you so much

OpenStudy (igreen):

No problem.

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