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Proportional and Non-Proportional Functions
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Key Concepts:
Terms in this set (26)
Direct Variation
A special type of linear relationship in which the ratio of any output value (y) to its corresponding input value (x) is proportional.
Constant of Proportionality (k)
The constant value of the ratio of two proportional quantities, general x and y, and written y=kx, where k is the factor of direct variation. (proportional coefficient of x)
Proportional Relationship
A linear relationship between 2 quantities in which one is a constant multiple of the other.
Relation
A set of input and output values.
Function
A relation for which each value from the independent set (domain/input) is associated with exactly one value from the dependent set (range/output).
Non-Proportional Relationship
A linear relationship between 2 quantities in which one is not a constant multiple of the other.
Slope
The numeric value that describes the rate of change for a linear function. (non-proportional coefficient of x)
Y-Intercept
The ordered pair where a line, curve, or surface intersect the y-axis and contains the x-coordinate of zero.
Slope-Intercept Form
A linear equation written in a form so that the slope (m) and y-intercept (b) are easily identified.
Independent Quantity
In a mathematical relationship, the independent quantity does not depend on another quantity or variable, but rather causes corresponding changes to the dependent quantity.
Dependent Quantity
In a mathematical relationship, the dependent quantity can take on different values only in response to its corresponding, independent quantity/variable.
Linear Relationship
The relationship between the independent and dependent quantities that form a straight line when graphed.
Linear Equation
An equation that represents a linear relationship.
output for graph
y-axis; dependent variable
input for graph
x-axis; independent variable
y-intercept for graph
location crossing the y-axis; can be (+) or (-)
output for equation
y variable; dependent variable
input for equation
x variable; independent variable
y-intercept for equation
follows the "x" term; can be (+) or (-)
input for table
x column/row; independent variable
output for table
y column/row; dependent variable
y-intercept for table
y value when x is zero; can be (+) or (-)
solution
any value(s) that makes an equation/ number sentence or inequality true when substituted for the unknown
verifying a solution
if an equation has one solution, it can be substituted back into the original equation and the equation will be true
system of linear equations
two linear equations with the same set of variables
solving a system of linear equations
graphically - When both equations are graphed on the coordinate plane, the lines are intersecting.
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