Algebra 1 Chapter 3 Flashcards

x-intercept: Point where a graph crosses the x-axis; occurs when y equals zero.
slope-intercept form: Linear equation format is y = mx + b, where m is the slope and b is the y-intercept.
linear equation: Equation producing a straight line on the coordinate plane.
positive slope: Describes a line that rises as it moves from left to right.
negative slope: Describes a line that falls as it moves from left to right.
zero slope: Characterizes a horizontal line that has no change in y; represented as y = constant.
undefined slope: Applies to vertical lines which do not change x; represented as x = constant.

function: Input-output relationship ensuring one output exists for each input.
slope: Ratio of vertical change (rise) to horizontal change (run); indicates the rate at which y changes with respect to x.
y-intercept: The point where a graph intersects the y-axis; occurs when x equals zero.

standard form: Linear equation format is Ax + By = C, where A and B are not zero and A is a whole number.
linear function: A function characterized by ordered pairs adhering to a linear equation.
parent function: The simplest linear function defined by f(x) = x.

Example slopes from specific equations:
- For y = 3x + 2, the slope is 3.
- For y = -2x - 8, the slope is -2.
To find y-intercepts:
- For y = 6x + 5, the y-intercept is 5.
- For y = 2x - 9, the y-intercept is -9.
For the equation 5x - 20y = 60, the slope is 1/4 and the y-intercept is -3.

direct variation: Expressed as y = kx, where k is the constant of proportionality and cannot be zero.
constant of variation: The steady rate of change in direct variation, represented as k.

sequence: An ordered list of numbers following a particular pattern.
arithmetic sequence: A sequence with a constant difference between consecutive terms, denoted as "d".
inductive reasoning: Drawing conclusions based on observed patterns from examples.