Direct Variation Rate of Change

9.4 Direct Variation Notes

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​9.4 Direct Variation

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​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.

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​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...

Multiple Choice

Which graph shows a relationship that varies directly?

Multiple Choice

Which graph shows a relationship that varies directly?

Multiple Choice

Which equation represents a relationship with direct variation?

• y = -3x

• y = 0.25x - 1

• y = 4x + 5

Multiple Choice

Which equation DOES NOT represent a relationship with direct variation?

• y = -7x

• y = 4x + 7

• y = 3.5x

​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

Multiple Choice

$$y=8x$$  What is the constant of variation? (aka slope)

• 8

• 8x

• cannot be determined without a graph

Multiple Choice

$$y=x$$  What is the constant of variation? (aka slope)

• -1

• cannot be determined without a graph

• 1

• 0

Multiple Choice

What is the constant of variation? (hint: think, how many miles per hour?)

• 5

• 2.5

• depends on the hour

• 3

Multiple Choice

What is the constant of variation? (hint: think, how dollars per hour?)

• 25

• 50

• 100

• 75

Multiple Choice

What is the constant of variation? (hint: think, how many miles per hour?)

• 6

• 2.5

• 1.2

• 1.5

• 3.2

Multiple Choice

Which equation represents the graph shown?

remember: In y= mx, m is the constant of variation (aka slope.)

• y = x

• y = 2x

• y = 2x + 1

• y = 1x

• y = (1/2)x

Multiple Choice

Which equation represents the graph shown?

remember: In y= mx, m is the constant of variation (aka slope.)

• y =2 x

• y = 12x

• y = 18x

• y = 1x

• y = 16x

Multiple Choice

y = 4x

Draw

just want to try this draw feature. doodle something, I guess.