Compare Proportional Relationships
Analyze linear equations
y = mx+b
y = mx+b
Compare linear and nonlinear functions
Intervals of Increase and Decrease
Sketch functions from verbal descriptions.
100
The table shows the rate at which Brianna sells homemade dog treats.
1) The number of dog treats and the cost are in a(n)____________________.
2) The dog treats sell at a(n)____________________of $4 for 2 treats.
1) Proportional relationship
2) Constant Rate
100
What is the term that best represents the item in each box.
Slope
100
Complete the vocabulary chart by supplying the definitions
y-intercept, where the function crosses the y-axis.
100
The graph of this function has four different ________________.
A negative slope means the function is________________.
In interval 3, the graph is flat so the function is___________________.
The function is increasing when the slope is____________________.
The graph of the function in interval 1 shows that the function is____________.
In interval 4, the slope of the function is____________________.
1) Intervals
2) Decreasing
3) Constant
4) Positive
5) Increasing
6) Decreasing
100
The values in the x column are________________ values.
Input
200
The graph shows the amount of savings over time in Eliana's account. Lana, meanwhile, puts $40 each week into her savings account. If they both begin with $0, who is saving at the greater rate?
Eliana saves at a greater rate because her unit rate of $42 per week is greater than Lana's unit rate of $40 per week.
200
The graph relates the number of gallons of white paint to the number of gallons of red paint Jess used to make the perfect pink. Write an equation that describes the relationship.
The equation y=(1/3)x describes the relationship
200
Complete the vocabulary chart by supplying the definitions
Not a straight line
200
Indicate which intervals are increasing, decreasing, or constant
Increasing? Answer: 1, 3, 6
Decreasing?
Answer: 2, 5
Constant?
Answer: 4
200
Write a situation which best describes the given graph. Use pencil and paper. Explain what you know about the function from the given graph.
The amount of money a company has goes up and then they have to pay their costs. This happens at the end of each month.
300
The table shows the rate at which Brianna sells homemade dog treats.
1) The equation y = 3x can be used to find the cost, y, for x dog treats sold by Cameron. Cameron sells dog treats at a rate that is ________________Brianna’s rate.
2) The point (4, 6) lies on the line that represents the rate at which Jessie sells dog treats. Jessie sells dog treats at a rate that is _________________Brianna’s rate.
1) Greater than
2) Less than
300
The graph shows a proportional relationship between the variables y and x. Write an equation to model the relationship. Use pencil and paper. Explain how you know there is a proportional relationship if you are given either an equation or a graph.
The equation y = 15x models the relationship.
300
Two linear functions are shown. Which function has the greater initial value?
Function A has the greater initial value because the initial value for Function A is 6 and the initial value for Function B is 5.
300
You have a device that monitors the voltage across a lamp in a certain circuit. The results are shown in the graph. Use the graph to classify intervals of behavior of the given function.
Interval (a) is a constant interval. Interval (b) is a decreasing interval. Interval (c) is a constant Interval. Interval (d) is an increasing interval.
300
Mathilda starts at her house and drives for 20 minutes to a friend's house. She stays there for 60 minutes. Let T be the time since Mathilda left the house, and S be the distance in miles from her house. Sketch a graph that shows the relationship between T and S. Use pencil and paper. Describe a situation that would also have a similar graph like the given situation.
400
Sam and Bobby want to know who cycled faster. The table shows the total miles Sam traveled over time. The graph shows the same relationship for Bobby. Who cycled faster?
Find the unit rate (constant of proportionality) for Sam.
Find the unit rate (constant of proportionality) for Bobby.
Bobby cycled faster.
400
Car X travels 144 miles in 3 hours.
a) Write the equation of the line that describes the relationship between distance and time. Use x for the time in hours and y for the distance in miles.
b) What is the graph that represents the relationship between distance and time for Car X? Explain.
a) The equation y=48x describes the relationship.
b)
If a car travels for 0 hours, it will travel 0 mile(s). This means it will pass through the point (0, 0). Use the slope to move 3 units to the right of the origin and 144 unit(s) up to find the point (3, 144) that can be used to graph the relationship.
400
Justin opens a savings account with $4. He saves $ 2 each week. The table represents his account balance. Decide whether the table represents a linear function or a nonlinear function
The table represents a linear function.
400
A signal generator is used to generate signals for a lab experiment. The graph shows the frequency of the signal generated. Use pencil and paper. Explain your answer.
1. How many decreasing intervals are defined in the graph?
2. How are the decreasing intervals alike?
3. How are the decreasing intervals different?
1) 2
2) All of the decreasing intervals indicate lengths of time when the frequency is decreasing. All of the decreasing intervals end at 0 Hz.
3) The decreasing intervals start from different frequencies.
400
a) What does the horizontal line represent for the given graph?
b) Describe a situation that matches the given graph.
a) The horizontal line represents that after a certain time the total number of people remains constant.
b) There is a game in a park. During the first few hours people continue to arrive. For the next few hours the number of people remains the same.
500
The amount of money, y, pizzeria L makes by selling x pizzas can be modeled by the equation y = 14x. The relationship of the amount of money pizzeria W makes is shown in the following graph. Which pizzeria makes more money per pizza?
Pizzeria L makes more money per pizza.
500
What term best represents the item.
Run or change in x
500
Which linear function has the greater rate of change, the one described by the equation y = 7x+3 or the one described by the table?
The function y=7x+3 has the greater rate of change.
500
Graph a function where interval (1) is a constant interval, interval (2) is a decreasing interval, interval (3) is an increasing interval, and interval (4) is a constant interval.
500
A baseball team scores a steady number of runs in each of the first 3 innings. After that they do not score a run the rest of the game, which lasts 10 innings. Let x represent the inning of the game, and y represent the total number of runs. Sketch a graph that shows the relationship between x and y. Use pencil and paper. What would happen to the graph if the innings in which they score runs changes?
