Questions and Answers
What does the term 'Positive' refer to in a coordinate system?
What does the term 'Negative' refer to in a coordinate system?
What is the x-axis?
The horizontal number line in a coordinate system
What is the y-axis?
Signup and view all the answers
What is the Origin?
Signup and view all the answers
An ordered pair consists of two numbers that are used to locate any point on a coordinate plane; it is represented as (____, ____).
Signup and view all the answers
What are Linear Equations?
Signup and view all the answers
How many answers does a linear equation have?
Signup and view all the answers
What is the Multiple Solutions Method?
Signup and view all the answers
What is the X and Y-intercepts Method?
Signup and view all the answers
What is Slope?
Signup and view all the answers
What is Gradient?
Signup and view all the answers
What is Slope-intercept form?
Signup and view all the answers
What is a Best Fit Line?
Signup and view all the answers
What are other names for a Coordinate Grid?
Signup and view all the answers
Study Notes
Key Concepts in Linear Equations
- Positive Values: Correspond to points above the x-axis and to the right of the y-axis.
- Negative Values: Correspond to points below the x-axis and to the left of the y-axis.
- x-axis: The horizontal line used to represent the independent variable in a coordinate system.
- y-axis: The vertical line used to represent the dependent variable in a coordinate system.
- Origin: The intersection point of the x-axis and y-axis, designated as (0,0).
- Ordered Pair: A pair of numbers in the form (x,y) that specifies a point's location on the coordinate plane.
Understanding Linear Equations
- Linear Equations: Equations that graph as straight lines, indicating a constant rate of change.
- Infinite Solutions: Linear equations have an unlimited number of solutions that satisfy the equation.
- Multiple Solutions Method: A graphical method involving creating tables of ordered pairs to identify and graph solutions to a linear equation.
- X and Y-intercepts Method: Solve for intercepts by setting y to zero to find the x-intercept and vice versa, creating a line from plotted points that represents infinite solutions.
Slope and Its Applications
- Slope: Measures the steepness of a line and is calculated as the ratio of vertical change (rise) to horizontal change (run) between two points.
- Gradient: A percentage representation of the slope, providing insight into the rate of change.
- Slope-intercept Form: A linear equation format, expressed as y = mx + b, where m is the slope and b is the y-intercept, useful for finding the slope and intercept quickly.
Data Representation
- Best Fit Line: A line drawn through a scatter plot that closely approximates the distribution of data points; useful for making predictions from the observed data.
- Coordinate Grid: Also known as the coordinate plane, coordinate system, or Cartesian plane, this is the spatial framework used for graphing linear equations and plotting points.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
This quiz covers key concepts in linear equations, including the significance of positive and negative values, the role of the x-axis and y-axis, and the definition of ordered pairs. Understanding the graphical representation of linear equations and their solutions is essential for mastering this topic.
