This is an example of a Linear Function. A linear function is a function where the ratio, change of output/change of input is constant over the entire domain of the function. Linear functions are those whose graph is a straight line. A linear function has the form y=a + bx. A linear function has one independent variable and one dependent variable. The independent variable is x and the dependent variable is y. A is the constant term or the y intercept. It is the value of the dependent variable when x = 0. B is the coefficient of the independent variable. It is known as the slope and gives the rate of change of the dependent variable. Also called slope intercept form which is y=mx+b where m is the slope and b is the y intercept. Point Slope Form of an equation is y-y1=m(x-x1). There also is a general form of the equation of a straight line which is ax+by+c=0. While all linear equations produce straight lines when graphed, not all linear equations produce linear functions. In order to be a linear function, a graph must be both linear (a straight line) and a function (matching each x value to only one y-value).
As early as 200 B.C. the Chinese had devised a clever method for solving systems of two linear equations with two unknowns. The history of modern linear algebra dates back to the early 1840's. In 1843, William Rowan Hamilton introduced quaternions, which describe mechanics in three-dimensional space. In 1844, Hermann Grassmann published his book Die lineale Ausdehnungslehre (see References). Arthur Cayley introduced matrices, one of the most fundamental linear algebraic ideas, in 1857. Despite these early developments, linear algebra has been developed primarily in the twentieth century.
As early as 200 B.C. the Chinese had devised a clever method for solving systems of two linear equations with two unknowns. The history of modern linear algebra dates back to the early 1840's. In 1843, William Rowan Hamilton introduced quaternions, which describe mechanics in three-dimensional space. In 1844, Hermann Grassmann published his book Die lineale Ausdehnungslehre (see References). Arthur Cayley introduced matrices, one of the most fundamental linear algebraic ideas, in 1857. Despite these early developments, linear algebra has been developed primarily in the twentieth century.
Linear Function Examples.docx | |
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Real Life Linear Functions.docx | |
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