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Questions and Answers
What does the abscissa refer to in the Cartesian coordinate plane?
What does the abscissa refer to in the Cartesian coordinate plane?
- The line that runs horizontally
- The first coordinate in an ordered pair (correct)
- The line that runs vertically
- The second coordinate in an ordered pair
Which of the following represents a linear equation in standard form?
Which of the following represents a linear equation in standard form?
- xy = 12
- y = 3x + 4
- x^2 + y^2 = 1
- 2x + 3y = 5 (correct)
Which of the following is a characteristic of a function?
Which of the following is a characteristic of a function?
- Each element in the domain pairs with exactly one element in the range. (correct)
- Each element of the range can pair with multiple elements of the domain.
- The domain always consists of integers only.
- The range can contain elements that are repeated.
What type of slope describes a line that rises from left to right?
What type of slope describes a line that rises from left to right?
Which of the following is not a valid representation of a relation?
Which of the following is not a valid representation of a relation?
Flashcards
Cartesian Coordinate Plane
Cartesian Coordinate Plane
A plane formed by two perpendicular number lines, called the x-axis and y-axis, used to graph points using coordinates.
Ordered Pair
Ordered Pair
A set of two numbers, written in a specific order (x, y).
Linear Equation (Standard Form)
Linear Equation (Standard Form)
An equation that produces a straight line when graphed, expressed in the form: ax + by = c, where a, b, and c are numbers, and x and y are variables.
Relation (Math)
Relation (Math)
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Function (Math)
Function (Math)
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Study Notes
Cartesian Coordinate Plane
- Descartes combined algebra and geometry.
- Ordered pairs (x, y) define points.
- X is the abscissa, Y is the ordinate.
- Standard linear equation form: ax + by = c, where a and b are not zero and exponents are one.
Linear Equations
- Solutions to linear equations in two variables can be represented as y = x + 2.
- A relation is a set of ordered pairs.
- Domain (x) is the set of all first coordinates.
- Range (y) is the set of all second coordinates.
Representing Relations
- Relations can be shown in three ways:
- Tables of values
- Mapping diagrams
- Graphs
Types of Relations
- One-to-one relation: Each domain value pairs with a unique range value.
- One-to-many relation: Domain values can repeat.
- Many-to-one relation: Range values can repeat.
Functions
- A function is a rule that pairs each domain element with exactly one range element.
- Domain values cannot repeat in a function.
Slopes of Lines
- Slope describes the direction of a line.
- Positive slope: Line goes up from left to right.
- Negative slope: Line goes down from left to right.
- Zero slope: Line is horizontal.
- Undefined slope: Line is vertical.
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