Graphing
How do you know a system of equations has infinite solutions by graphing?
The lines are coinciding
y = 4x + 2
4x - 3y = 18
(-3, -10)
x + y = 14
6x + 2y = 0
(-7, 21)
You went downtown with your family and decided to rent Segways to roam around town. It costs $25 to rent a Segway, and the $ 0.10 per minute you are riding it.
a) Define the independent and dependent variables.
b) Write a linear equation function to model the cost of your Segway adventure.
a) Independent (x) - # of minutes
Dependent (y) - Cost in dollars
b) y = .10x + 25
What did Mr. Doll look like when he first started teaching at GCHS?
Solve the systems by graphing. The graph of each function must have 5 precise points.
f(x) = 3x - 4
y = 3
(2.33,3)
f(x) = 5x - 11
g(x) = 5(x - 3) + 4
Infinite Solutions
4y + x = 10
-3y + 5x = -19
(-2, 3)
You sell Build-a-Bears and Baby Reborn Dolls on the dark web as a side gig to fund your Boba Tea addiction. On Dark Web Wednesday, you sold a total of 73 toys and made $5360 (That's a lot of Boba). You charge $22 for a bear, and a doll costs $43.
Write a system of equations that could be used to determine the number of each toy you sold (DO NOT SOLVE).
B = # Bears ; D = # Dolls
B + D = 73
22B + 43D = 5360
The equation t = 6m +13 models the total cost, t, in dollars to drive m miles in an uber. The total cost consists of a flat flee plus a charge per mile driven. When the equation is graphed, what does the y-intercept of the represent in terms of the model?
a) a flat fee of 13 dollars
b) a charge per mile of 6 dollars
c) a charge for mile of 13 dollars
d) total daily charges of 29 dollars
e) none of the above
A
Solve the systems by graphing. The graph of each function must have 5 precise points.
y - 4 = -2(x + 1)
f(x) = -2x + 10
No Solutions (Lines are parallel)
6x - 4y = 15
-6x + 7y = 18
(9.83, 11)
3y = 18 - 6x
-10x - y = 26
(-4, 14)
PHQ is an analytical tool used to determine the level of enjoyment Pandas experience when they are living in a Zoo (PHQ - Panda Happiness Quotient). Since Pandas' main activity in life is eating, zoologists were able to study and determine that the Panda's PHQ increased .78 points for every 1 pound of bamboo they consumed. They also factored in a starting PHQ value of 4.27 based on the average amount of time Pandas sleep during the day.
Answer the following:
1) What is the RoC cooking in this situation?
2) What are the independent and dependent variables?
3) Write an equation which would model a Panda's PHQ.
1) .78 PHQ per 1 pound of Bamboo
2) Ind (x) = lbs of Bamboo ; Dep (y) = PHQ Score
3) P(x) = .78x + 4.27
What form is strongly recommended to use when we have an independent and dependent relationship?
Slope-Intercept Form
f(x) = mx + b
or
y = mx + b
Solve the systems by graphing. The graph of each function must have 5 precise points.
2x - 6y = 18
y = 3x - 7
(1.5, -2.5)
9x - 4y = 63
4y + 5x = -21
(3, -9)
2x - 3y = 12
-9y + 6x = -20
No Solutions
During a vacation to Washington DC you visited the International Spy Museum and decided your life goal was to become a spy for the CIA! During your first undercover mission in Iran, you got a job as a maintenance worker in a Nuclear Power Station, which would pay you 31,580 rials an hour. You were also given an equipment stipend of 50,000 rials each week to purchase the necessary work clothing. (Rial is the national currency in Iran)
Create a linear equation to model how much rial you would make in a week.
RoC = 31,580 rial per 1 hour
x = # of hours ; f(x) = # of Rial
f(x) = 31,580x + 50,000
What do you look for in a situation that tells you to use Standard Form to write an equation for your system? (Standard Form is also known as Vecna Form in the Upside Down)
Totals that involve the variables
Solve the systems by graphing.
f(x) = -x2 - 4x - 1
g(x) = 2x + 7
(-2, 3) and (-4, -1)
y= 20 - 2x
-10x - 5y = 60
No Solutions
-7x - 3y = -5
5x + 6y = 19
(-1, 4)
Amiyah is starting a Traveling Hair Salon Business, and she has found two companies that offer hair care product packages (which Amiyah needs to use for her clients): Harry's Hair Supply and Brenda's Braid Company.
Harry is going to charge Amiyah $172.50 per package and required an annual membership fee of $375. Brenda charges $207.25 for the same package, but no membership fee.
Under what conditions would Harry's Hair Supply be the best option for Amiyah and her business?
x: # packages ; y:$ cost
y = 172.50x + 375
y = 207.25x + 0
Solution: (10.79, 2236.51)
Harry's is a better option for 11 packages or more.
What do you get when you mix Vegeta Violet and Bulma Blue? (This is why you should pay attention to my jokes in class!!!)
Trunks Turquoise