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Linear Functions by Gabi Dumond

math
by

Gabi D

on 2 January 2014

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Transcript of Linear Functions by Gabi Dumond

3- Plants
I 'm going to fill my garden with yellow floribunda roses. These flowers will be perfect for my garden because yellow is one of the colors that represents Coventry. Also, the rose flower is the flower of June. This will represent Coventry well because Captain Nathan Hale's birthday is in June, and since the flower of June is roses, I will fill the garden with yellow floribunda roses. Roses are the best flower for my garden because roses are not a high-maintenance flower and they are perennial flowers, so they will grow back every year. Also, roses can be planted in almost any zone (mostly zones 6-9), which means they can be planted in Coventry, zone 6a. I will buy the yellow floribunda roses at parkseed.com.
1- Filling Material
I will fill the garden with mulch. This mulch will be rubber, so no weekly maintenance is required. Also, this mulch will be in the color green, one of the colors that represents Coventry. I will get the green rubber mulch shipped to the work site from the Home Depot in Manchester Connecticut. Lastly, I believe this is the best material for this garden because the mulch doesn't attract insects of any kind, the mulch prevents weeds, and the mulch saves money by not needing weekly care.
4- Cost of Plants
My plants will cost $19.00 per yellow rose bush, with a $7 delivery charge. Each rose bush is about 2/3 of a yard, so I will be buying 24 rose bushes to fit my sketch. So overall, I will be buying $456.00 worth of yellow rose bushes (22 yards of rose bushes), with the additional $7 delivery charge. This altogether equals $463.00.
6-Function for Total Cost
5- Continued
This garden will represent Coventry well for many reasons. First, the triangle shape of the garden represents the shape of Captain Nathan Hale's hat. Second, the shape the rose bushes are in the shape of our town, Coventry. Third, the roses are the flower of June, and Captain Nathan Hale's birthday is in June, so the roses are to represent Captain Nathan Hale, our hero. Lastly, the color of the mulch and the flowers together are the colors of our wonderful town, Coventry.
8- Thickness
I 'm going to lay the material two inches thick to cover the garden. I decided on this thickness by doing some research and the website I found said it is best to lay mulch two inches thick.
Linear Functions
5- Visual Representation
10 yards
7- Slope and y-intercept
The slope of the function for the material represents the cost of material per cubic yard, or the rate per cubic yard. The y-intercept of the function for the material represents the delivery charge for the material no matter how much material you buy, even though the y-intercept is zero in this case.
2- Cost of Material
The cost of the green rubber mulch is $271.26 per cubic yard. There is no delivery charge for the shipping of the green rubber mulch.
By: Gabi Dumond
Class A
Mr. Stegman

Zone Map
Zone Temperatures
googleimages.com
Coventry's Zone
homedepot.com
parkseed.com
The green mulch was in cubic feet, but I had to transfer it to cubic yards. There is 76.9 cubic feet of material being sold for $773.10. I transferred this into cubic yards by dividing the amount of cubic feet, 76.9, by 27 because there are 27 feet in 1 cubic yard. (For example, there are 3 feet in 1 yard, but we're talking about cubic yards, so this means we have to take the 3 feet and put it to the third power (cubed). In result, this gets me 27 feet in 1 cubic yard (3^3= 3*3*3=27)).This got me 2.85, rounded, cubic yards. Then, I took the total price for 76.9 cubic feet, $773.10, and divided it by 2.85 to get the unit price of how much money it costs per cubic yard, $271.26 (rounded).
10 yards
10 yards
4 yards
4 yards
2 yards
3 yards
1 yard
2 yards
4 yards
2 yards
yellow= rose bushes
green= mulch
The thickness of the green mulch will be two inches thick.
Height= 8.66 Yards
I wrote a separate function for the material and the flowers. These are slope-intercept form functions (functions that contain a slope (rate)and a y-intercept (starting value)) because they contain a slope and a y-intercept.
Material:
Y= 271.26x + 0
total cost for the material
cost per cubic yard
variable (how much material you want)
delivery charge (which is free, so we don't need to add the zero)
Flower:
Y= 19x + 7
total cost for the rose bushes
cost per rose bush
variable (how many rose bushes you want)
delivery charge
orange= slope
dark blue= y-intercept
Since I made two functions, I have to add the total cost for the material and the flowers together at the end to get the total cost for the garden.
The slope-intercept form formula is
Y= mx +b
y= total amount
m= slope
b= y-intercept
x= variable
8.66 yards
Area= 43.3 yards squared
dark blue= height
The slope of the function for the flowers represents the cost per rose bush, or the rate per rose bush. The y-intercept of the function for the flowers represents the delivery charge for the flowers no matter how many rose bushes you buy.
www.gardenguides.com
I will need 86.6 cubic yards of material for my garden.
Area= 43.3 yards squared
Since the area covers the ground all over in one layer, I have to multiply it by two because I 'm laying the material two inches thick.
9- Total Cost
The total cost of my garden will be $23,954.12
Material:
Y=271.26x + 0
original function
Y= 271.26 (86.6) + 0
Y= 23,491.12 +0
Y= 23,491.12
Flower:
Y= 19x + 7
original function
Y= 19 (24) + 7
Y= 456 + 7
Y= 463
6 rb
rb= rose bushes
2 rb
0 rb
6 rb
2 rb
2 rb
2 rb
4 rb
463
+ 23,491.12
10- Thickness Cut
11- Form of Function
I used the slope-intercept form function to write my cost function. This form was most useful to me because the information within the function had a rate and a start value (parts of a slope-intercept function). This was also very useful because if I had used the other form, standard form (combination problems), I wouldn't have been able to fit both the slopes and y-intercepts into the one function.
Slope Form
Standard Form
C= ax + by
Y= mx + b
Combination Problems
Rate Problems
12- Converting Functions
$23,954.12
rounded from 23,491.116
I will need 43.3 cubic yards of material if the thickness of the original material is cut in half.
86.6/2= 43.3 cubic yards
original thickness
the cut in half
new amount of material
This does half the price of my garden because the price of the flowers is so little compared to the price of the mulch, and the price of material is almost the whole price.
Y= 271.26 (86.6) + 0
Y= 271.26 (43.3) + 0
original
new (half material)
Y= 11,745.56
rounded from 11,745.558
11,745.56 + 463 =
$
12,208.56
from $23,954.12
Since my original equation is in slope-intercept form, I will transfer it to standard form.
Y= 271.26x + 0
Y= 19x + 7
original equations
slope-intercept form
A standard form equation is also referred to as combination problems because they deal with two different parts.
C= ax + by
standard form

C= 271.26x + (19y + 7)
material cost
flower cost with delivery charge
variables
total cost
The meaning of this equation is to fit both parts, rate of material and flowers, into one equation and to make less work to do.
The End!!!!!!!
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