Linear Equations, Intercepts, and Forms

Vocabulary and definition flashcards covering Standard Form, Intercepts, and Point-Slope Form based on linear equation lecture notes.

Standard Form

A linear equation written as $Ax + By = C$, where $A$, $B$, and $C$ must be integers that have no common factor greater than $1$ (except in a word problem), and the leading coefficient $A$ must be positive.

x-intercept

Also called the Zero; the location where the function ($y$-value) has a value of $0$ and the line crosses the $x$-axis. It is written in the form (#, 0).

y-intercept

The location where the line crosses the $y$-axis and $x = 0$. It is written in the form (0, #).

Finding an x-intercept

To find an $x$-intercept without a graphed line, substitute a $0$ for $y$ and solve for $x$.

Finding a y-intercept

To find a $y$-intercept without a graphed line, substitute a $0$ for $x$ and solve for $y$.

Point-Slope Form

A linear equation form defined as $y - y_1 = m(x - x_1)$, where $m$ is the slope, $x_1$ is the $x$-value of the coordinate point, and $y_1$ is the $y$-value of the coordinate point.

Steps to Writing an Equation in Point-Slope Form

1. Calculate the slope if not given. 2. Using one point and slope, substitute $x$, $y$, and $m$ into the formula without distributing. 3. Simplify the double negatives if needed.