Lesson 4: 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 $Ax + By = C$. Linear equations have infinitely many solutions.
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.

Examples

• The equation $5x + 2y = 10$ is a linear equation in two variables, with $A=5$, $B=2$, and $C=10$.

• The equation $y = 4x - 3$ is a linear equation. It can be rewritten in standard form as $4x - y = 3$.

Property

1. The equation of the horizontal line passing through $(0, b)$ is

2. The equation of the vertical line passing through $(a, 0)$ is

Examples

• The equation of the horizontal line passing through the point $(4, 7)$ is $y = 7$. Every point on this line has a y-coordinate of 7.
• The equation of the vertical line that contains the point $(-2, 5)$ is $x = -2$. Every point on this line has an x-coordinate of -2.
• The x-axis is a horizontal line with the equation $y=0$, and the y-axis is a vertical line with the equation $x=0$.

Explanation

For a horizontal line, every point has the same height (y-value), so its equation is just $y$ equals that constant value. For a vertical line, every point is the same distance left or right (x-value), so its equation is $x$ equals that constant value.