Lesson 5: Graphing Linear Equations in Standard Form

Property

An equation of the form $Ax + By = C$, where $A$ and $B$ are not both zero, is called a linear equation in two variables.

A linear equation is in standard form when it is written $Ax + By = C$.

An ordered pair $(x, y)$ is a solution of the linear equation $Ax + By = C$, if the equation is a true statement when the $x$- and $y$-values of the ordered pair are substituted into the equation.

Property

To convert a linear equation to slope-intercept form $y = mx + b$, solve the equation for $y$ by isolating $y$ on one side of the equation.

Examples

Property

To graph a linear equation using the intercepts:
Step 1. Find the $x$-intercept by setting $y = 0$ and solving for $x$.
Step 2. Find the $y$-intercept by setting $x = 0$ and solving for $y$.
Step 3. Plot both intercepts on the coordinate plane.
Step 4. Draw a straight line through the two points.

Examples