Equation of a Line Passing Through Two Points

Vocabulary flashcards covering the key definitions, formulas, and forms required to determine the equation of a line passing through the points (-5, 1) and (5, -3).

Slope formula

The formula $m = \frac{y_2 - y_1}{x_2 - x_1}$, used to calculate the rate of change or slope between two points $(x_1, y_1)$ and $(x_2, y_2)$.

Slope of the line passing through $(-5, 1)$ and $(5, -3)$

The slope $m = -\frac{2}{5}$, found using the ratio $\frac{-3 - 1}{5 - (-5)} = \frac{-4}{10}$.

Slope-intercept form

A linear equation written in the form $y = mx + b$, where $m$ represents the slope and $b$ represents the $y$-intercept.

Point-slope form

A linear equation expressed as $y - y_1 = m(x - x_1)$, where $m$ is the slope and $(x_1, y_1)$ is a given point on the line.

Standard form of a linear equation

A linear equation written in the format $Ax + By = C$, where $A$, $B$, and $C$ are integers and $A$ is typically non-negative.

$y$-intercept of the line through $(-5, 1)$ and $(5, -3)$

The point $(0, -1)$, or $b = -1$, where the line crosses the $y$-axis.

Slope-intercept equation of the line through $(-5, 1)$ and $(5, -3)$

The equation $y = -\frac{2}{5}x - 1$.

Point-slope equation using point $(-5, 1)$

The linear equation $y - 1 = -\frac{2}{5}(x + 5)$.

Point-slope equation using point $(5, -3)$

The linear equation $y + 3 = -\frac{2}{5}(x - 5)$.

Standard form equation of the line through $(-5, 1)$ and $(5, -3)$

The equation $2x + 5y = -5$.