Linear Relationships and Slope

​Linear Relationships and Slope

By Maria Durham

Linear Relationships

Linear relationships show a constant rate of change meaning we add or subtract the sam amount over and over again.

Situations that show a constant rate of change: Zalyn adds $50 to her savings every single week.

​​Examples of Linear Relationships

Situations that do not show a constant rate of change: JT doubles the money in his account each week.

​​Examples of Non-Linear Relationships

The table shows a constant rate of change. Money increases by $40 every 5 car washes.

The graph shows a constant rate of change. Sales increases by $1000 every 3 days.

The table does not show a constant rate of change. The amount added is different each time.

The graph does not show a constant rate of change. They go 6 m/s then 4 m/s.

Multiple Choice

Is this relationship represented by the graph Linear or Nonlinear

• linear

• nonlinear

Multiple Choice

Is the relationship represented by the table linear or nonlinear?

• Linear

• Nonlinear

Multiple Choice

Is the relationship represented by the table linear or nonlinear?

• linear

• nonlinear

Multiple Choice

Is the relationship represented by the graph linear or nonlinear

• linear

• nonlinear

Multiple Choice

Which answer choice is true?

• The table represents a linear relationship because there is a pattern for the x-coordinates and y-coordinates.

• The table represents a linear relationship because the ratio of the change in the y value and the change in the x value is constant.

• The table represents a nonlinear relationship because the ratio of the change in the y value and the change in the x value is not constant.

Multiple Choice

Which graph is linear?

• A

• B

• C

• D

Multiple Choice

Why is this relationship linear?

• This is a linear relationship because it does not have a constant rate of change

• This is a linear relationship because it creates a curved line.

• This is a linear relationship because it have a constant rate of change.

• This is a linear relationship because it's y-intercept is (0,2)

Multiple Choice

Is the relationship represented by the table linear or nonlinear?

• Linear

• Nonlinear

Multiple Choice

Is the graph pictured a linear or nonlinear function?

• Linear
• Nonlinear

Multiple Choice

Is this relationship linear or nonlinear?

A tree is 4 feet tall and grows 2 feet each year.

• Linear

• Nonlinear

Multiple Choice

Is this relationship linear or nonlinear?

The temperature starts at 70°F and drops 8°F every hour.

• Linear

• Nonlinear

Multiple Choice

Is this relationship linear or nonlinear?

The number of buds on a tree in the spring triples each week.

• Linear

• Nonlinear

Slope

The constant rate of change in a linear relationship is called the slope. The slope can be described as the rise/run or the change in y/change in x.

Finding Slope

In a table, find the differences and divide. The slope is 3/2.

In a graph, find the rise and run. Or you can make a table using 2 points on the line. The slope is 3/2

When finding the slope between 2 points, make a little table then find your differences and divide.

Describing Slope

We can describe slope as positive, negative, zero, or undefined.

Positive slope shows a line that increases as we read left to right.

Zero slope shows a horizontal line. In this case the "rise" = 0 and 0 divided by any number is 0.

Undefined slope shows a vertical line. In this case the "run" = 0 and any number divided by 0 is undefined.

Negative slope shows a line that decreases as we read left to right.

Multiple Choice

Find the slope of the line that passes through the points ( 6, 3) ( 7, - 4)

• -7

• 7

• 6

• -6

Multiple Choice

Find the slope of the line that passes through the points ( 6, - 2 ) ( 5, - 4 )

• 3

• -3

• 2

• -2

Multiple Choice

Find the slope of the line that passes through the points ( 7, - 4) (4 , 8 )

• 5

• -5

• 4

• -4

Multiple Choice

Find the slope of the line that passes through the points (5, 9 ) ( 3, 9 )

• 0

• undefined

• 1

• 2

Multiple Choice

Find the rate of change

• 45/1

• 1/5

• 5

• -5

Multiple Choice

What is the slope of the line? Be sure to simplify.

• 3/4

• 1/2

• -3/4

• 2

Multiple Choice

Find the slope of the line

• -3/4

• 3/4

• 4/3

• -4/3

Multiple Choice

Slope is best described as_________________

• steepness of a line

• length of a line

• width of a line

• Height of a line

Multiple Choice

What kind of slope is this?

• Positive

• Negative

• Zero

• Undefined

Multiple Choice

What kind of slope is this?

• Positive

• Negative

• Zero

• Undefined

Match

Match the graph description with the correct slope

• Horiztional Line

• Vertical Line

• UpHill Line

• DownHill Line

0

Undefined

2

-5

• 0

• Undefined

• 2

• -5

Multiple Choice

What is the slope of the line represented by the table?

• 0

• undefined

• 5

• 2

• 2/5

Multiple Choice

What is the slope of this line?

• Positive

• Negative

• Zero

• Undefined