Section 1.4: Linear Equations Basics
A linear equation is an equation in which the variable(s) appear only to the first power, and the graph of the equation is a straight line.
General Form:
A linear equation in one variable looks like: \( ax + b = c \), where \( a \), \( b \), and \( c \) are constants and \( a \neq 0 \).
In two variables, the general form is: \( Ax + By = C \).
Example 1
Determine if the following is a linear equation: \( 3x + 5 = 11 \).
The variable \( x \) is raised only to the first power, so this is a linear equation in one variable.
Example 2
Is \( y = 2x^2 + 1 \) linear?
No. The variable \( x \) is squared, so this is a quadratic equation, not linear.
Practice Problems
- Identify if \( 7x - 4 = 10 \) is linear or not.
- Which of the following are linear equations? a) \( 5y + 3 = 12 \) b) \( x^2 - 7 = 0 \) c) \( 4x - 9 = 2x \)
- Write an example of a linear equation in one variable.
- Write an example of a linear equation in two variables.
- Explain why \( xy = 6 \) is not linear in two variables.