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Flashcards on Direct Proportionality Functions
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What are direct proportionality functions?
Functions where the dependent variable is directly proportional to the independent variable.
How can direct proportionality be represented algebraically?
Using the equation y=kx, where k is the constant of proportionality.
What do the graphs of direct proportionality functions look like?
They form a straight line passing through the origin (0,0).
What happens to the dependent variable when the independent variable increases in direct proportionality functions?
The dependent variable also increases.
What happens to the dependent variable when the independent variable decreases in direct proportionality functions?
The dependent variable also decreases.
What is the slope of the graph of a direct proportionality function?
The slope is equal to the constant of proportionality.
In direct proportionality functions, what happens to the ratio of dependent variable to independent variable?
The ratio is constant, i.e. it does not change.
What is an example of a real-life situation that can be modeled by a direct proportionality function?
The distance traveled by a car and the time taken, when the car is moving at a constant speed.
How can the constant of proportionality be determined from a table of values?
By dividing the value of the dependent variable by the value of the independent variable for any point on the table.
What is the general form of a direct proportionality function?
y = kx
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Test Your Knowledge
In direct proportionality functions, what happens to the dependent variable when the independent variable increases?
It also increases
It decreases
It remains constant
It varies randomly
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What is the equation commonly used to represent direct proportionality functions?
y = x^2
y = kx
y = mx + b
y = -x
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What can be stated about the ratio of dependent variable to independent variable in direct proportionality functions?
The ratio is constant
The ratio increases
The ratio decreases
The ratio varies randomly
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What kind of line is formed by the graph of a direct proportionality function?
Curved line
Straight line
Vertical line
Horizontal line
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What is the slope of the graph of a direct proportionality function?
Positive slope
Negative slope
Equal to the constant of proportionality
Undefined slope
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For a direct proportionality function, if the value of the independent variable is halved, what happens to the value of the dependent variable?
It is also halved
It doubles
It remains the same
It becomes zero
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Which of the following situations can be modeled by a direct proportionality function?
The height of a growing plant and the amount of rainfall
The volume of a gas and the pressure, at constant temperature
The price of a product and the demand
The speed of a moving object and the time taken
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What is the constant of proportionality in the equation y = 5x?
5
x
-5
0
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What happens to the dependent variable in a direct proportionality function when the value of the independent variable is zero?
It becomes negative
It is also zero
It becomes undefined
It remains constant
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What is the general form of a direct proportionality function?
x = ky
y = kx
y = mx + b
y = -x
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