How can a linear equation be defined?

How can a linear equation be defined?

• A. An equation with one variable only
• B. An equation that has exponents greater than one
• C. An equation with no exponents greater than one
• D. An equation that results in a constant

Answer: (C)

A linear equation can be defined as an equation that represents a straight line when graphed, which is characterized by having a maximum exponent of one for all the variables involved. This means that the equation can be written in the form of \( y = mx + b \) or \( ax + by = c \), where \( m \) and \( b \) are constants, and \( a \), \( b \), and \( c \) are coefficients. The absence of exponents greater than one ensures that the relationship between the variables is linear; it maintains a consistent slope and does not curve, which is essential for identifying a linear function. Thus, the definition aligns perfectly with this foundational concept in algebra.

A linear equation can be defined as an equation that represents a straight line when graphed, which is characterized by having a maximum exponent of one for all the variables involved. This means that the equation can be written in the form of ( y = mx + b ) or ( ax + by = c ), where ( m ) and ( b ) are constants, and ( a ), ( b ), and ( c ) are coefficients. The absence of exponents greater than one ensures that the relationship between the variables is linear; it maintains a consistent slope and does not curve, which is essential for identifying a linear function. Thus, the definition aligns perfectly with this foundational concept in algebra.