Questions and Answers
What is the form of a linear function?
What characterizes a linear equation?
Each term is either a constant or the product of a constant and a single variable.
What is a dependent variable?
A variable that is measured and affected during an experiment.
What is an independent variable?
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What does the y-intercept represent?
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What is an x-intercept?
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What is the standard form of a line?
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What describes the slope of a line?
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What is the point-slope equation?
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What is the slope-intercept form of a line?
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Horizontal lines are parallel to the horizon.
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Vertical lines are parallel to the horizon.
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What are perpendicular lines?
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What defines parallel lines?
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An undefined slope corresponds to a vertical line.
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A positive slope indicates a line that is decreasing.
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A line with a negative slope trends upward from left to right.
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A zero slope describes a horizontal line.
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Study Notes
Linear Functions and Equations
- Linear functions have a graph represented by a straight line, expressed as y = f(x) = a + bx.
- A linear equation is an algebraic equation where each term is either a constant or a product of a constant with a single variable raised to the first power.
Variables
- The dependent variable is affected by changes in the independent variable and is what is measured during an experiment.
- The independent variable is changed by the scientist to observe its effect on the dependent variable, ensuring a fair test by only varying one independent variable at a time.
Intercepts
- The y-intercept (b) of a line is the value of y when the line crosses the y-axis in the linear equation y = mx + b.
- The x-intercept is the point on the graph where y equals zero.
Line Representations
- Standard form of a line is represented as Ax + By = C, where A is a positive integer, and B and C are integers.
- Slope (m) indicates the steepness and direction of a line, with definitions for increasing, decreasing, horizontal, or vertical slopes.
Equation Forms
- Point-slope form of a linear equation is y − y1 = m(x − x1), using a known point on the line (x1, y1) and the slope (m).
- Slope-intercept form is given as y = mx + b, highlighting the slope and the y-intercept.
Line Characteristics
- Horizontal lines run from left to right and are parallel to the horizon, defined as having a zero slope.
- Vertical lines are perpendicular to the horizon and have an undefined slope due to the invariant x-coordinate, creating no "run."
- Perpendicular lines intersect at right angles, while parallel lines never intersect or touch.
Slope Types
- A positive slope indicates an increasing line, while a negative slope indicates a decreasing line.
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Test your knowledge with these flashcards on Linear Functions and Linear Equations from Algebra 2 Chapter 2. Understand the definitions and forms of linear relationships. Perfect for studying and reinforcing key concepts in algebra.
