text: in math, (algebra) what is the definition of many soloutions? & what is the general form of a linear equation?   a linear equation is an equation involving only the sum of constants or products of constants and the first power of a variable. such an equation is equivalent to equating a first-degree polynomial to zero. these equations are called "linear" because they represent straight lines in cartesian coordinates. a common form of a linear equation in two variables is  y = mx + c  (e.g. y = 3x + 5) in this form, the value m will determine the slope or gradient of the line; and the value c will determine the point at which the line crosses the y-axis. equations involving terms such as x2, y1/3, and xy are "non-linear".