Key Features
How do you find the domain?
x-values
left to right
Solve the system by graphing
y = x + 4
y = 2x + 5
(-1,3)
The solution to the system of equations:
x + y = -6
x - y = -10
What is (-8, 2)?
x = 4y
2x + 3y = 22
Set up the system of equations.
Two kids at a summer camp, Anthony and Philip, are competing in a potato sack race. Anthony is younger, so he is given a head start of 8 yards. When the race starts, Anthony hops at a rate of 1 yard per second, and Philip hops 2 yards per second.
y=x+8
y=2x
How do you find increasing intervals?
Positive slope
x-values
y = 3x - 2
y = -x - 2
The solution to the system:
8x + 5y = 18
2x - 5y = -8
What is (1, 2)?
y = x - 2
3x - y = 16
Set up the system of equations.
Two classmates got together over the weekend to do their assigned History reading. Devin can read 1 page per minute, while Greta can read 3 pages per minute. When they met, Devin had already read 96 pages, and Greta had already gotten through 8 pages.
y=x+96
y=3x+8
How do you find the average rate of change from a graph?
Slope
rise/run
y = -3
x = 5
The solution to the system:
2x + 3y = 6
3x + 5y = 15
What is (-15, 12)?
y = 3x - 1
7x + 2y = 37
Set up the system of equations.
Mario's Pizza just received two big orders from customers throwing parties. The first customer, Rodrigo, bought 3 regular pizzas and 6 deluxe pizzas and paid $117. The second customer, Vicky, ordered 3 regular pizzas and 1 deluxe pizza, paying a total of $47.
3x+6y=117
3x+y=47
How do you find the negative intervals?
Below the x-axis
x-values
y = (1/3)x - 3
2x - y = 8
The solution to the system
2x - 4y = 12
-8x + 16y = -48
What is infinitely many solutions?
The solution to the system
3x - 2y = 4
y = 2x - 1
What is (-2, -5)
Set up the system of equations.
Zach and Chandler are hosting events that are catered by the same company. Zach plans to have 93 adults and 32 children attend, so the total projected cost of his meals is $3,520. Chandler has 79 adults and 32 children on his guest list, so he will pay the caterer $3,072.
93x+32y=3520
79x+32y=3072
y - 3x = 3
y = 3x - 2
The solution to the system:
4x + 3y = 120
2x - 3y = 24
What is (24, 8)
The solution to the system
x + y = 12
3x = y
What is (3, 9)?
Set up the system of equations.
An online boutique is having a special on personalized baby items. On Monday, they sold 15 personalized baby blankets and 19 personalized hooded towels, for a total of $861 in receipts. The following day, they received orders for 19 personalized baby blankets and 5 personalized hooded towels, which brought in a total of $633.
15x+19y=861
19x+5y=633