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In this expression, $a$ and $b$ are real numbers, with $a =0.$ To completely understand the definition of a linear expression, some important concepts will be be broken down. Consider the example linear expression $x−5y+2.$

$x−5y+2$ | ||
---|---|---|

Concept | Explanation | Example |

Term | Parts of an expression separated by a $+$or $−$sign. |
$x,$ $-5y,$ $2$ |

Coefficient | A constant that multiplies a variable. If a coefficient is $1,$ it does not need to be written due to the Identity Property of Multiplication. | $1,$ $-5$ |

Linear Term | A term that contains exactly one variable whose exponent is $1.$ | $x,$ $-5y$ |

Constant Term | A term that contains no variables. It consists only of a number with its corresponding sign. | $2$ |

The following table shows some examples of linear and non-linear expressions.

Linear Expressions | Non-linear Expressions |
---|---|

$3x$ | $5$ |

$-5y+1$ | $2xy−3$ |

$3x−21 y+2$ | $x1 −2$ |

$πx+6y$ | $5x_{2}+x−1$ |

$3x+4−2x+9−x=13 $

The expression $3x+4−2x+9−x$ looks like a linear expression, but the result after simplifying is $13,$ which is a constant and therefore not a linear expression.