Algebra 2 Chapter 2 Flashcards

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.