Two ocean beaches are being affected by erosion. The table shows the width, in feet, of each beach at high tide measured where 1995 is represented by year 0.

- JozelynW

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- JozelynW

Describe the patterns shown by the erosion data measurements shown for each of the beaches in the table.
Between which years will the beaches have approximately the same width?
Assuming these rates remain constant, what can you do to get a better approximation of when the two beaches will have the same width?

- JozelynW

Year number Western Beach width (in feet) Dunes Beach width (in feet)
0 100 20
5 90 45
10 80 70
11 78 75
12 76 80
15 70 95

- JozelynW

@peachpi please helppp

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## More answers

- CBARREDO1

Western Beach is losing sand, Dunes beach is gaining sand.
Between 11 and 12 years
Plot the data against time and draw a curve that goes through the data. Where the two lines cross is the time when both beaches are the same width.

- JozelynW

ok i think you are correct does anyone agree with him.

- JozelynW

I don't need to get anything wrong

- anonymous

@CBARREDO1 is correct

- JozelynW

ok thanks

- JozelynW

You are such a great person I always count on you to help me with me with math @peachpi thanks a lot.

- anonymous

You're welcome. Thank you! I appreciate that :)

- CBARREDO1

I feel left out here ;-;

- JozelynW

and thanks to you as well c

- JozelynW

so @CBARREDO1 is this your paper or did you just do this tooday

- JozelynW

because i don't want to copy

- anonymous

@CBARREDO1 don't feel left out. you did all the hard work! :)

- JozelynW

yea definitely i just messaged him

- CBARREDO1

what paper are you talking about?

- JozelynW

the problem response you gave me

- CBARREDO1

No, I just analyzed, where could I copy it from xD?

- JozelynW

@CBARREDO1 how would i graph this on geogbra

- JozelynW

any one knows

- CBARREDO1

What's geogbra?

- JozelynW

ldo you know what is desmos

- JozelynW

@peachpi do you know how to graph on geogbra

- JozelynW

or desmos

- CBARREDO1

I know desmos

- JozelynW

ok how on desmos. i don't know hot to graph point only equations

- anonymous

sorry I don't know geobra. I don't really know how to do points on desmos.

- JozelynW

cant be mad cause i don't know either.

- anonymous

you can make equations for the lines by hand or use wolframalpha to get the line between points. then graph the lines on desmos

- JozelynW

ok let me see

- JozelynW

im on the website and i dont know where to go

- anonymous

Go to wolframalpha.com
There should be a box to type in.
Enter this to get an equation for the first beach: line through (0,100) and (5,90)

- JozelynW

k

- JozelynW

it says y=100-2x

- JozelynW

well is their another 2 point to do?

- CBARREDO1

put that equation in desmos, and then the line comes do the same for the next

- anonymous

^yep

- JozelynW

wait but aren't we trying to figure out the approx for year 11 and 12

- JozelynW

when they will be the same width

- JozelynW

approximation of when the two beaches will have the same width?

- anonymous

that's why you're graphing them. once you have the lines graphed you're looking for the intersection point, which will be between 11 and 12

- JozelynW

but 0,100 is is year 0 while 5,90 is year 5. Year 11 and 12 are the closest, so should't we be doing year 11 and 12 then finding where intersection point is?

- JozelynW

and how will we have two lines

- JozelynW

please talk back

- JozelynW

@peachpi WHAT HAPPENED

- anonymous

sorry didn't realize you had posted something here. You're going to have 2 different equations, one for each beach. We found the first equation is y = 100 - 2x.
Find the second one using 2 points from the other beach, like (0, 20) and (5,45).
As far as choosing 11 and 12, it doesn't matter. It takes 2 points to define a line, it doesn't matter which two points you use. You can use the points that correspond to 11 and 12 and the results will be the same. I just picked the two I chose because they were the top two points.

- JozelynW

I COPY AND PASTED JUST AS IT IS HERE SO IT IS Y=5X+20 sorry about caps

- anonymous

ok. so the two lines you're going to graph are y = 5x + 20 and y = 100-2x

- anonymous

and you're looking for the intersection point

- JozelynW

it is (11.43,77.14)

- anonymous

yes

- JozelynW

ok thank you

- anonymous

youre welcome

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