Linear Equations, Intercepts, and Line Relationships

Vocabulary practice flashcards covering slope-intercept form, point-slope form, standard form, intercepts, horizontal/vertical lines, and parallel and perpendicular line relationships.

Point-Slope Form

A form of linear equation written as $y - y_1 = m(x - x_1)$, which allows you to write the equation of a line without knowing the y-intercept by using any two points to find the slope $m$ and any one point $(x_1, y_1)$.

Slope-Intercept Form

A linear equation written in the form $y = mx + b$, where $m$ is the slope (calculated as $\frac{\text{Rise}}{\text{Run}}$) and $b$ represents the y-intercept at the coordinate $(0, y)$.

Standard Form

A linear equation written in the form $Ax + By = C$, which is useful when writing out word problems and provides the easiest format for finding the x-intercept and the y-intercept.

Parallel Lines

Lines in the same plane that never intersect; they share the exact same slope, but have different y-intercepts.

Perpendicular Lines

Lines that intersect to form right angles; their slopes are opposite reciprocals of each other.

Opposite Reciprocals

Two numbers whose signs are opposites and whose numerators and denominators are inverted (such as $-\frac{1}{4}$ and positive $\frac{4}{1}$ or $4$); this relationship describes the slopes of perpendicular lines.

Slope Formula

The mathematical formula $m = \frac{y_2 - y_1}{x_2 - x_1}$, used to determine the slope $m$ of a line given any two points $(x_1, y_1)$ and $(x_2, y_2)$.

y-intercept

The point where a line crosses the y-axis, which always has the coordinate $(0, y)$; it is found by substituting $0$ for $x$ and solving the equation for $y$.

x-intercept

The point where a line crosses the x-axis, which always has the coordinate $(x, 0)$; it is found by substituting $0$ for $y$ and solving the equation for $x$.

Slope in Standard Form

A shortcut method to determine the slope of an equation written in standard form $Ax + By = C$, given by the ratio $m = -\frac{A}{B}$.

Zero Slope

The slope of a horizontal line that occurs when an equation has no $x$-term. Linear equations simplify to the form $y = c$ , where c is a constant (such as $2y = 6$ or $y = 3$).

Undefined Slope

The slope of a vertical line that occurs when an equation has no $y$-term, simplifying to the form $x = c$, where c is a constant (such as $3x = -6$ or $x = -2$).