​continue when you have the title written on your notes page

​>>>>>>

​9.4 Direct Variation

​continue when you have written the definition

​>>>>>>

​9.4 Direct Variation

​A direct variation is a relationship in which the ratio of y to x is constant (in other words the slope, m, is constant)

​We say y varies (changes) directly with x.

​continue when you are done writing

​>>>>>>

​9.4 Direct Variation

​A direct variation is a relationship in which the ratio of y to x is constant (in other words the slope, m, is constant)

​We say y varies (changes) directly with x.

​

​* The graph of a relationship with direct variation will ALWAYS:

​1.

​2.

​continue when you are done writing

​>>>>>>

​9.4 Direct Variation

​A direct variation is a relationship in which the ratio of y to x is constant (in other words the slope, m, is constant)

​We say y varies (changes) directly with x.

​

​* The graph of a relationship with direct variation will ALWAYS:

​1. be a straight line

​2. go through the origin (0, 0)

​continue when you are done writing

​>>>>>>

​9.4 Direct Variation

​A direct variation is a relationship in which the ratio of y to x is constant (in other words the slope, m, is constant)

​We say y varies (changes) directly with x.

​

​* The graph of a relationship with direct variation will ALWAYS:

​1. be a straight line

​2. go through the origin (0, 0)

​

*The equation of this kind of relationship will always be in the form y = mx (m refers to the slope (or in this case, the constant of variation)

​continue when you are done writing AND answering the example

​>>>>>>

* The graph of a relationship with direct variation will ALWAYS:

​1. be a straight line

​2. go through the origin (0, 0)

​

*The equation of this kind of relationship will always be in the form y = mx (m refers to the slope (or in this case, the constant of variation)

​Example:

​The speed of a sloth can be represented with the equation y=6x This relationship is shown in the graph below. Explain how you know the relationship between distance and time is a direct variation. Then state the constant of variation.

​

Correct your explanation/answers if needed.

​>>>>>>

* The graph of a relationship with direct variation will ALWAYS:

​1. be a straight line

​2. go through the origin (0, 0)

​

*The equation of this kind of relationship will always be in the form y = mx (m refers to the slope (or in this case, the constant of variation)

​Example:

​The speed of a sloth can be represented with the equation y=6x This relationship is shown in the graph below. Explain how you know the relationship between distance and time is a direct variation. Then state the constant of variation.

​

​Answers:

✔The graph is a straight line which goes through the origin. (Alternative explanation: the equation is in the form y = mx)

​✔The constant of variation is 6

​(here, this represents 6 ft/min)

Notes are completed.

The remaining exercises do not have to be written in your notebook. Rather, they are for practice...

​recall:

​in the equation form y = mx

​m: slope (or constant of variation)

​

​for example: y = 5x means each y value is 5 times as much as each x value