Linear Equations and Proportional Relationships

Vocabulary terms and definitions covering linear equations, slope, intercepts, and proportional relationships.

Linear equation

An equation whose graph is a line.

Origin

The point where the $x$ and $y$ axes intersect, located at $(0, 0)$ on the graph.

Proportional relationship

A relationship where there is a constant rate in one variable as the other variable increases by $1$, represented by an equation in the form $y = mx$ that passes through the origin.

Slope

The rise over run, or the change in $y$ over the change in $x$ when moving from one point on the line to another point on the line, which describes the steepness and angle of the line.

$y$-intercept

The value of $y$ when $x = 0$ (represented by $b$), which shifts the line up and down the $y$-axis and makes the equation not proportional if added or subtracted.

Slope-intercept form

The equation form $y = mx + b$, where $m$ is the slope and the proportional line part ($y = mx$) is shifted up or down along the $y$-axis by the $y$-intercept ($b$).

Undefined slope

The slope of a vertical line that goes straight up without moving horizontally over.

Rise

The vertical change, or difference in $y$-values, between two points on a line.

Run

The horizontal change, or difference in $x$-values, between two points on a line.

Negative slope

The slope of a line that moves downwards to the right, as opposed to a positive slope which moves upwards to the right.