A linear equation is an algebraic equation in which each variable is raised to the power of 1, meaning the highest exponent of the variable is always 1. It can have one or more variables, but none of the variables are multiplied together or raised to powers greater than one
. Key characteristics of linear equations:
- They represent straight lines when graphed on a coordinate plane.
- In one variable, the standard form is Ax+B=0Ax+B=0Ax+B=0, where AAA and BBB are constants and xxx is the variable.
- In two variables, the standard form is Ax+By=CAx+By=CAx+By=C, where AAA, BBB, and CCC are constants and xxx, yyy are variables.
- The graph of a linear equation in two variables is always a straight line.
- The slope of the line indicates how steep the line is and whether it rises or falls as you move from left to right
Additional notes:
- Linear equations describe relationships where the value of one variable depends linearly on the other.
- They are fundamental in algebra and are widely used in mathematics, physics, and engineering because many nonlinear systems can be approximated by linear equations
In summary, a linear equation is an equation that forms a straight line when graphed, with variables raised only to the first power and no products of variables involved. It can be expressed in forms such as Ax+B=0Ax+B=0Ax+B=0 or Ax+By=CAx+By=CAx+By=C, depending on the number of variables
