Understanding Linear Relationships and Equations
Flashcard
•
Mathematics
•
6th Grade
•
Practice Problem
•
Hard
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1.
FLASHCARD QUESTION
Front
What is a linear relationship?
Back
A linear relationship is a relationship between two variables that can be represented by a straight line on a graph. It can be expressed in the form of an equation, such as y = mx + b, where m is the slope and b is the y-intercept.
2.
FLASHCARD QUESTION
Front
What does the slope of a line represent in a linear equation?
Back
The slope of a line represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how much y changes for a unit change in x.
3.
FLASHCARD QUESTION
Front
What is the y-intercept in a linear equation?
Back
The y-intercept is the point where the line crosses the y-axis. It is the value of y when x is 0, represented as (0, b) in the equation y = mx + b.
4.
FLASHCARD QUESTION
Front
How can you identify dependent and independent variables in a linear relationship?
Back
The independent variable is the one that is manipulated or changed (usually x), while the dependent variable is the one that responds to the change (usually y).
5.
FLASHCARD QUESTION
Front
What does the equation y = 32x represent in a real-world context?
Back
It represents a situation where an employee earns a total of y dollars at a rate of $32 per hour for x hours worked.
6.
FLASHCARD QUESTION
Front
What is the difference between the equations y = x + 8 and y = 8x?
Back
In y = x + 8, y is 8 more than x. In y = 8x, y is 8 times the value of x.
7.
FLASHCARD QUESTION
Front
How do you plot a point on a coordinate grid using an ordered pair?
Back
To plot a point using an ordered pair (x, y), start at the origin (0, 0), move x units along the x-axis, and then move y units up (if y is positive) or down (if y is negative).
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