Linear Equations and Slope: Vocabulary Flashcards

Vocabulary flashcards covering key concepts from the lecture notes on linear equations, slope, and line forms.

Linear equation

An equation whose graph is a straight line; its solutions form a line in the plane.

Graph of a linear equation

The straight line in the plane that represents all solution pairs (x, y) satisfying the equation.

Two points determine a line

Any line is uniquely defined by two distinct points on it.

Slope

The rate of change of y with respect to x; the ratio Δy/Δx (rise over run), describing the line’s steepness and direction.

Delta y

The change in the y-coordinate between two points on a line.

Delta x

The change in the x-coordinate between two points on a line.

Rise

The vertical change between two points on a line (the Δy in rise over run).

Run

The horizontal change between two points on a line (the Δx in rise over run).

Zero slope

A horizontal line, where the slope is 0 (no vertical change).

Undefined slope

A vertical line, where the slope is not a real number (infinite).

Standard form

A linear equation written as Ax + By = C, with A, B, C real numbers.

Slope-intercept form

The linear equation written as y = mx + b, where m is the slope and b is the y-intercept.

Function form

Another expression of a linear equation, typically y = mx + b, emphasizing y as a function of x.

Coefficient of x (m)

In y = mx + b, m is the slope of the line.

Y-intercept

The point where the line crosses the y-axis (b in y = mx + b).

X-intercept

The point where the line crosses the x-axis (the solution when y = 0).

Horizontal line

A line with zero slope; y remains constant as x varies.

Vertical line

A line with undefined slope; x remains constant as y varies.