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Questions and Answers
What is a linear function?
What is a linear function?
A function whose graph forms a straight line
What is a linear equation?
What is a linear equation?
Any equation that can be written in the standard form Ax + By = C
What is an x-intercept?
What is an x-intercept?
The x-coordinate of the point where the graph intersects the x-axis
What is a y-intercept?
What is a y-intercept?
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What is the rate of change?
What is the rate of change?
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What is rise in the context of a graph?
What is rise in the context of a graph?
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What is run in the context of a graph?
What is run in the context of a graph?
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What is slope?
What is slope?
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What is direct variation?
What is direct variation?
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What is the constant of variation?
What is the constant of variation?
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Study Notes
Linear Functions and Equations
- A linear function presents a graph that forms a straight line, depicting a constant rate of change.
- Linear equations can be expressed in the standard form (Ax + By = C), where A, B, and C are constants.
Intercepts
- The x-intercept is where the graph meets the x-axis, characterized by a y-coordinate of 0.
- The y-intercept occurs where the graph intersects the y-axis, noted by an x-coordinate of 0.
Change and Slope
- The rate of change measures the variation in the dependent variable against the independent variable, providing insights into relationships between them.
- Rise is defined as the difference in the y-values between two points on a line, indicating vertical change.
- Run represents the difference in the x-values of two points on a line, reflecting horizontal change.
- Slope is calculated as the ratio of rise to run, representing the steepness and direction of the line.
Variations
- Direct variation occurs when there is a linear relationship expressed in the form (y = kx), indicating that y changes directly with x.
- The constant of variation (k) in the equation (y = kx) is a nonzero constant that represents the proportional relationship between y and x.
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Description
Test your knowledge of key concepts from Algebra Chapter 4 with these flashcards. You'll encounter definitions for linear functions, equations, and intercepts. Perfect for reinforcing your understanding of these fundamental topics.
