Linear Relationships

Linear Relationships

y=mx+b

Reviewing Proportional Relationships

y=kx

Multiple Choice

A comparison of two quantities by division is...

Example: 2 to 4

• Ratio

• Rate

Multiple Choice

A ratio of two quantities that have different units.

Example: 8 ounces in 1 cup

• Ratio

• Rate

Multiple Choice

A statement that two rates or ratios are equivalent.

Example: 2/4 = 1/2

• Ratio

• Rate

• Proportion

Multiple Choice

What is a constant ratio of two variables that are related proportionally?

Example: k=y/x, where k>0 or K<0.

• ratios

• unit rates

• constant of proportionality

• rate of change

Multiple Choice

What is the mathematical statement that two expressions are equal?

• expression

• equation

• operation

• variables

Multiple Select

Understanding Vocabulary

Proportional Relationship: a special type of linear relationship in which the rate of change is constant, or one in which the ratio of one quantity to the other is constant.

constant means "unchanging"

• True

• False

How do you use tables and verbal descriptions to describe a linear relationship?

*Look for patterns and describe them.

Linear Relationships

y=kx or y = x + b

*For any given situation (constant rate of change), we use pictorials, verbal descriptions, tables, graphs, numbers and equations in the form.

A set of data is displayed in any or all forms.

Linear Relationships (extending constant of proportionality)

y=kx

y=x+b

y=mx+b

Linear Relationships: y=mx+b

• As one quantity changes by a constant amount, the other quantity also changes by a constant amount.

• There are two variables.

• x and y

• The "x" variable is independent - manipulated.

• The "y" variable is dependent - responding.

• As one variable increases or decreases, the other variable has a corresponding increase or decrease.

• Example: When cooking for friends, the amount of food you need to prepare increases as the number of friends increases.

y=mx+b

m = constant rate of change

y = coordinate

x = coordinate = "0"

b = simplify (0,y)

How to represent Linear Relationships?

Charia orders T-shirts from a Web site that charges $8 per shirt. She also chooses expedited shipping that costs an additional $15.

How to represent Linear Relationships?

Charia orders T-shirts from a Web site that charges $8 per shirt. She also chooses expedited shipping that costs an additional $15.

Multiple Choice

Which equation represents the linear relationship shown in the table?

• y= x + 2

• y= 2x + 5

• y= x + 6

• y = 3x + 2

Multiple Choice

You are visiting Houston, Texas and a taxi cab company charges a flat rate of $4.00 for using the cab and $0.95 per mile.  Write an equation to determine the cost when x miles is driven.

• y = .75x
• y = .95x
• y = .95x + 4
• y=4.95x

Multiple Choice

A holiday meal costs $12.50 a person plus a delivery fee of $30.

• y = 12.5x+30

• y = 12.5 + 30

• y = 12.5 + 30x

Multiple Choice

Bob has $150 in his savings account and saves $40 per month.

• y = 150 + 40

• y = 40x + 150

• y = 150x + 40

Multiple Choice

You earn $18 for every hour you work. Which equation represents this function?

• y=(18/2)x + 0
• y = 18x
• y = 2x + 18
• y = 18x + 2

Multiple Choice

A driving range charges $4 to rent a golf club plus $2.75 for every bucket of golf balls you hit. Write an equation that shows the total cost c of hitting b buckets of golf balls.

• c = 2.75b + 4
• c = 2.75b
• c =  4b- 2.75
• c = 2.75b - 4

Multiple Choice

What is the equation of the line?

• y = 20x
• y = x + 20
• y = 2x
• y = x + 2

Multiple Choice

What is the equation for this table?

• y=3x+1

• y=4x-2

• y=x+1

• y=x+7

Multiple Choice

What is the constant of Proportionality for this table?

• 1/9
• 9
• 8

Multiple Choice

Is the graph proportional or non proportional?

• proportional
• non proportional
• both
• neither

Multiple Choice

Is the graph proportional or non proportional?

• proportional
• non proportional
• both
• neither

Multiple Choice

What is the constant of proportionality (in miles per hour) based on the table?

• 45
• 90
• 135
• 2

Multiple Choice

What is the rate of change (unit rate) for the following graph?

• 80
• 20
• 40
• 160

Multiple Choice

Choose the best explaination

• Taylor can write 6 words per minute
• Taylor can write 25 words per minute
• Taylor can write 50 words per minute
• Taylor can write 150 words per minute

Multiple Choice

Nancy can type 50 words per minute. Look at the table below to write an equation that matches the data.

• m=50 + w
• w= 50m
• w= 50 + m
• m= 50 - w

Multiple Choice

Does the chart represent a proportional or non-proportional relationship?

• proportional

• non-proportional

Multiple Choice

Which equation matches the table?

• y = x 
• y = 5x
• y = x - 4
• y = x + 4

Multiple Choice

The following points are located on a graph:

(0, 0) (1, 5) (2, 10) (5, 25)

What is the equation that represents these points?

• y = 3x

• y = x + 4

• y = 5x

• y = 3x + 2