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Questions and Answers
What is a linear function?
What is a linear function?
- A function with multiple variables
- A function with a vertical graph
- A function that forms a curve
- A function whose graph is a line (correct)
What does a linear equation represent?
What does a linear equation represent?
Linear functions
What is Y called?
What is Y called?
Dependent variable
What is X called?
What is X called?
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What is the y-intercept?
What is the y-intercept?
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What is the x-intercept?
What is the x-intercept?
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What is the standard form of a linear equation?
What is the standard form of a linear equation?
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What is slope?
What is slope?
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What is point-slope form?
What is point-slope form?
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What is slope-intercept form?
What is slope-intercept form?
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Study Notes
Linear Functions and Equations
- A linear function is characterized by a graph that is a straight line.
- A linear equation is an algebraic expression that represents linear functions.
Variables
- The dependent variable is represented by Y, which changes based on the value of the independent variable.
- The independent variable is denoted as X, which is the variable that can be controlled or changed.
Intercepts
- The Y-intercept is the point where the graph of the function intersects the y-axis.
- The X-intercept is the point at which the graph intersects the x-axis.
Standard Form
- The standard form of a linear equation is expressed as Ax + By = C, where A, B, and C are real numbers, and A and B cannot both be zero.
Slope
- The slope of a line is defined as the ratio of vertical change to horizontal change, illustrating how steep the line is.
Equation Forms
- Point-slope form of a linear equation is written as y - y1 = m(x - x1), where m is the slope and (x1, y1) is a specific point on the line.
- Slope-intercept form of a linear equation is expressed as y = mx + b, where m is the slope and b is the Y-intercept.
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