Slope and Y-Intercept
Graphing Linear Equations
Proportional vs Non-Proportional
Direct Variation
Systems of Equations
100
What is the slope of this line?
7/3
100
A line has a slope of -1/4 and y-intercept of -2. What is the equation of this line in slope intercept form?
y=-1/4x-2
100
In regards to each representation, how can you identify if the linear relationships is proportional?
equation: y=kx
table: ratio of y/x is constant
graph: linear and passes through the origin
100
Situations that vary directly can be represented by an equation, write down this equation.
y=kx
100
Complete the sentence, "the point of intersection of two graphed equations is the ___ of the system of equations, or the ___ ___ that makes both equations true"
Solution
Ordered Pair
200
In regards to each representations, what ways can you calculate or find y-intercept?
Graph: where line crosses the y-axis
Table: y-value when x-value is zero
Equation: b
Word problem: key words
200
What two pieces of information is needed to write an equation in slope intercept form?
Slope and Y-intercept
200
In regards to each representation, how can you identify if a linear relationships is non-proportional?
equation: y=mx+b
table: ratio of y/x is NOT constant
graph: NOT linear or does NOT pass through the origin
200
Fill in the blank, "the value of y __ __ with __"
"the value of y varies directly with x
200
Solve this system of equations by graphing. First graph the equations, and then type the solution.
y= –7/2x + 2
y= –2x – 1
300
In regards to each representation, in what ways can you calculate slope?
Graph: rise/run, slope formula
Table: change in y/x, slope formula
Equation: m/k
Word problem: key words
300
A line has coordinates (4,6) and (7,1) and y-intercept of 4. What is the equation of this line in slope intercept form?
y=-5/3x+4
300
Trevor's space shuttle crew accidentally left him behind on a mysterious planet. He soon realizes that his body is aging much faster on this planet than it did on Earth. There is a proportional relationship between the number of years he ages, y, and the number of weeks Trevor spends on the planet.
After 3 weeks on the planet, Trevor's body has aged 30 years. Write the equation for the relationship between x and y. Finally, calculate how many weeks would it take for Trevor to reach age 67.
y=10x
x=6.7
300
The value of y varies directly with x. If x = 15 and y = –90. Write a direct variation equation that represents the situation.
y=-6x
300
Solve this system of equations by graphing. First graph the equations, and then type the solution.
y= 4x + 3
x= –1
400
What famous magician died on Halloween in 1926?
Harry Houdini
400
What is the equation of this line in slope intercept form?
y= 1/2x - 3
400
Gio found a small online shop that sells Funko Pops to collectors all over the country. Each Funko Pop costs $13.00, and the store charges a flat shipping fee of $9.00.
He has a $100 gift card to spend and wants to know exactly how many Funko Pops she can purchase, including shipping costs.
Write an equation that models the total cost, y, for buying x Funko Pops.
Use your equation to determine how many Funko Pops Maya can buy without going over her $100 gift card.
y= 13x+9
x=7
400
If y varies directly with x and y= 16 when x=8, find y when x=4.
y=8
400
RANDOM QUESTION:
In 2005, Disney Channel produced a movie about twin witches who had been separated at birth, (the same actresses, ironically, starred in a show where they had also been separated at birth) who come together to fight the forces of evil. Who are the actresses who played these witches?
Tia and Tamera Mowry
500
Find the slope of the line that passes through points (-2,1) and (-2,4)
m= 3/0
Undefined
500
It was a chilly Halloween evening, and three math teachers — Mr. Pervis, Mr. Hankins, and Mr. Sindt — decided to turn their annual faculty costume contest into a “Mathematical Candy Expedition.” Instead of just giving candy to students, they wanted to collect candy donations from trick-or-treaters to raise money for the Math Club’s new “Haunted Graphing Calculator Fund.”
Each teacher began at different times, but as always, they decided to track their progress in the most algebraic way possible.
Mr. Pervis, dressed as a haunted protractor, started with 50 pieces of candy already donated from his first-period students. He realized that for every 15 minutes he spent visiting classrooms and greeting students in costume, he collected an additional 12 pieces of candy.
After an hour, Mr. Hankins, dressed as a walking coordinate plane, asked how his collection was going. He laughed and said, “I can model my candy collection, y, based on how long I’ve been collecting, x, in minutes!”
Write an equation in slope-intercept form to represent Mr. Pervis’s candy collection. (Simplify or put as decimal)
y=4/5x+50
or
y=0.8x+50
500
Portia wants to subscribe to a meal delivery service, and she's deciding between Appetizing Adventures and Comfort Kitchen. With both services, there is a proportional relationship between the number of servings a customer orders and the total cost of the order. Appetizing Adventures charges $108 for 9 servings.
This equation, y = 13x, describes how much Comfort Kitchen charges. In the equation, y represents the cost in dollars for x servings.
Which company charges less per serving?How much less does that company charge per serving?
Appetizing Adventures charges $1 less per serving
500
A person’s weekly pay is directly proportional to the number of hours worked. Shawn’s pay is $123.00 for 20 hours of work. Find the amount of pay for 31 hours of work.
y= 190.65
500
Quincy and Monica were playing basketball together. Her score was 30 points, and his score was 10 points. Quincy wanted to make the game more fair, so he called a time-out and modified the rules a bit. Quincy explained that, for the rest of the game, he would get 2 points per basket, and Monica would get 3 points per basket. Then they played a bit longer. After the time-out, they both made the same number of baskets and ended up with a tied score. How many points did each person have at the end? Let numbers of baskets be represented by x and number of points be represented by y.
y= 2x + 30
y= 3x = 10
70 Points