Linear equations are equations whose only terms are constants and/or single variables raised to the first power. More than one variable is allowed in a linear equation, but it is not allowed to be multiplied with another variable. Constants are allowed to be multiplied to variables in linear equations. These equations are called "linear" due to the fact that their solution set forms a line when represented in classic Euclidean space, e.g. when graphed on the mutually perpendicular x, y, and z axes of the Cartesian coordinate system.
Here are three examples of linear equations:
Slope-intercept form:
y = mx + b, where x is the independent variable, y is the dependent variable, and m and b are constants. This representation of a linear equation is useful because the slope of the line formed by its solution set is m.
Point-slope form:
y - y1 = m(x - x1), where x is the independent variable, y is the dependent variable, and m is the constant slope. The point (x1,y1) is included in this form to explicitly show that the independent distances of x and y between two points are proportional to each other by the proportionality constant, m, the slope.
Intercept form:
x/a + y/b = 1, where x and y are variables and a and b are non-zero constants. This form is useful because the x and y intercepts, i.e. the points on a graph where this line crosses the x and y axes, are a and b, respectively.
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All linear equations are functions but not all functions are linear equations.
There is no quadratic equation that is 'linear'. There are linear equations and quadratic equations. Linear equations are equations in which the degree of the variable is 1, and quadratic equations are those equations in which the degree of the variable is 2.
A system of linear equations.
To solve linear equations, you always use the inverse operations
You simplify the brackets first and then you will have linear equations without brackets!