Comparing Increasing and Decreasing Linear Functions

Comparing Increasing and Decreasing Linear Functions

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3 Questions

Multiple Choice

What is the slope of the equation 5X-2Y=18

• -5/2

• 5/2

• -10

• 10

Multiple Choice

What is the initial value of the equation Y-3=-7X?

• 7

• -7

• 3

• -3

Multiple Choice

What is the meaning of the point (0.5,0) on the graph?

• The tree grew at a rate of 0.5 foot per year

• The tree was 0.5 foot tall when it was planted

• Jacob planted the seed 0.5 foot below the ground

• The tree started growing above ground 0.5 year after Jacob planted the seed

Graph: a diagram showing the relation between variable quantities; a diagram representing a connection or relationship among two or more things by a number of distinctive plots, lines, bars, etc. 

Proportional Relationships: relationship between two variables where their ratios are equivalent 

Interpreting: explain the meaning of (information, words, action) 

Unit Rate: a ratio that compares units of one quantity to one unit of another quantity 

Slope: a number that describes both the direction and the steepness of the line 

Solve: to apply an operation(s) in order to find a value; to find an answer 

Real-world: relating to a concrete setting 

Mathematical: related to the abstract science of number, quantity and space 

Problems: a question that needs a solution 

Compare: examine the differences between numbers, quantities or values to decide if it is greater than, smaller than or equal to another quantity 

Represented: to show or model; to express or to stand for 

Develop: to cause to grow and become more mature, advanced, or elaborate 

Rate of change: slope; the ratio of the vertical change to the corresponding horizontal change in the coordinate plane 

Property: a mathematical rule; a character or attribute that something has 

Function - a relation in which every domain(input) value is paired with exactly one range(output) value

Vocabulary

SWBAT compare two different proportional relationships represented in different ways IOT solve real-world and mathematical problems. 8.EE.B.5 

SWBAT develop the idea of rate of change (slope) IOT compare properties of two functions each represented in a different way. 8.F.A.2

PBO

Open Ended

A two-person research submarine starts at the ocean surface and begins to descend. The equation d=-30t gives the submarine’s elevation in meters as a function of time in minutes. At the same time, a whale begins to ascend. The whale’s elevation at different times is given in the table.

What is the difference in the submarine’s elevation and the whale’s elevation at 0 minutes? Is the submarine or the whale traveling at a faster speed?

Open Ended

What is the difference in the submarine’s elevation and the whale’s elevation at 0 minutes? *I'm looking for a number*

Open Ended

2a. Speed is never negative. The whale’s rate of change is positive, but the submarine’s is negative. What does the sign of each rate represent in this situation?

b. Write an inequality statement comparing the absolute values of the rates. Is the submarine or the whale traveling at a faster speed?

c. Suppose the submarine’s rate changes to 272 meters per minute. The whale’s rate stays the same. Describe the direction each is moving. Which is traveling faster? Explain.

d. Suppose the whale is traveling at an average rate of 230 meters per minute and the submarine is traveling at an average rate of 225 meters per minute. Describe the direction each is moving. Which is traveling faster? Explain

Multiple Choice

A small-business owner has two bank accounts. The first is a payroll account. The equation P=45,000-2,500w represents the dollar amount in the payroll account as a function of time in weeks. The second account has $8,000 at Week 0, and the business owner deposits $1,500 each week. What is the total amount in the two accounts at Week 0?

• $53,000

• $37,000

• $45,000

• $42,500

Multiple Select

Which statement is true? Select all that apply.

• The initial value of an increasing function is always less than the initial value of a decreasing function.

• You can use rate of change to compare functions.

• A line representing an increasing function will always be steeper than a line representing a decreasing function.

• Absolute value can help you compare rates of change when at least one of the functions is decreasing.

• The initial value of a proportional relationship is always 1.

Open Ended

What is the difference in the initial values of the functions in the Example?

Open Ended

Demi teaches drum classes. The equation B=50t gives the dollar amount she earns as a function of the time in hours she teaches. Demi also takes spin classes. The graph shows how much she has left on a gift card as a function of the time in hours Demi is in class. Does Demi earn more teaching 1 hour of drum class or spend more taking 1 hour of spin class? Show your work.

Open Ended

A marine biologist and her colleague are scuba diving. The marine biologist begins to ascend. At the same time, her coworker begins to descend. The graph shows the marine biologist’s change in elevation over time. The table shows the colleague’s elevation at different times.

a. How far apart are the marine biologist and her coworker at t=0?

b. Is the marine biologist or her coworker moving faster? Show your work.

c. A student and the marine biologist are together at t=0. The student ascends more slowly than the marine biologist. Write an equation of a function that could represent the student’s ascent.

Word Cloud

Summarize today's lesson in 1-2 sentences

Multiple Choice

Is function represented by the table linear or nonlinear?

• linear
• nonlinear

Multiple Choice

What do we know about the slope for increasing functions?

• The slope is positive

• The slope is negative

• There is zero slope

Multiple Choice

Linear functions can be written in the form:

$$y=mx+b$$  
What is the rate of change?

• y

• m

• x

• b

Multiple Choice

Linear functions can be written in the form:

$$y=mx+b$$  
What is the initial value?

• y

• m

• x

• b

Multiple Choice

Determine if the following functions are increasing or decreasing.

• Both functions are decreasing.

• The function in item I is increasing, and the function in item II is decreasing.

• The function in item I is decreasing, and the function in item II is increasing.

• Both functions are increasing.

Multiple Choice

Which graph is linear?

• Graph A
• Graph B
• Graph C
• Graph D

Multiple Choice

Is the graph increasing or decreasing

• Increasing

• Decreasing

Multiple Choice

Is the graph increasing or decreasing

• Increasing

• Decreasing