Linear Functions Formula
linear functions Formula is an algebraic equation in which each term is either a constant or the product of a constant and (the first power of) a single variable. For example, a common equation, , (namely the slope-intercept form, which we will learn more about later) is a linear function because it meets both criteria with and as variables and and as constants. It is linear: the exponent of the term is a one (first power), and it follows the definition of a function: for each input ( ) there is exactly one output ( ). Also, its graph is a straight line.
Graphs of Linear Functions Formula
The origin of the name “linear” comes from the fact that the set of solutions of such an equation forms a straight line in the plane. In the linear function graphs below, the constant,, determines the slope or gradient of that line, and the constant term, , determines the point at which the line crosses the -axis, otherwise known as the -intercept.
Vertical and Horizontal Lines
Vertical lines have an undefined slope, and cannot be represented in the form, but instead as an equation of the form for a constant , because the vertical line intersects a value on the -axis, . For example, the graph of the equation includes the same input value of for all points on the line but would have different output values, such as etcetera. Vertical lines are NOT functions, however, since each input is related to more than one output.
Horizontal lines have a slope of zero and is represented by the form,, where is the -intercept. A graph of the equation includes the same output value of 6 for all input values on the line, such as , etcetera. Horizontal lines ARE functions because the relation (set of points) has the characteristic that each input is related to exactly one output.