Lesson 3: Standard Form

Property

A linear equation in standard form is written as $Ax + By = C$, where $A$, $B$, and $C$ are real numbers, and $A$ and $B$ are not both zero.
This is one of the most useful forms for linear equations because it clearly shows the relationship between the variables and makes certain calculations easier.

Examples

Property

To convert from slope-intercept form $y = mx + b$ to standard form $Ax + By = C$, rearrange the equation so that all variable terms are on the left side and the constant is on the right side. Ensure that $A$, $B$, and $C$ are integers with no common factors.

Examples

Property

To graph a linear equation using the intercepts:
Step 1. Find the $x$- and $y$-intercepts of the line.
• Let $y = 0$ and solve for $x$
• Let $x = 0$ and solve for $y$.
Step 2. Plot the two intercepts.
Step 3. Draw the line through the intercepts.

Examples

Property

A vertical line is the graph of an equation of the form $x = a$. The line passes through the $x$-axis at $(a, 0)$.
In this type of equation, the value of $x$ is always equal to $a$, no matter the value of $y$.

Examples

• The graph of the equation $x = 5$ is a vertical line where every point has an x-coordinate of 5, such as $(5, 0)$, $(5, 2)$, and $(5, -3)$.
• The equation $x = -2$ represents a vertical line that passes through the x-axis at the point $(-2, 0)$.
• A vertical line that passes through the point $(7, 4)$ has the equation $x = 7$ because the x-coordinate must always be 7.

Explanation

When an equation only has an $x$ variable, like $x = 2$, it means $x$ is always fixed at that number. No matter how high or low you go on the y-axis, the result is a perfectly straight, up-and-down vertical line.