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Linear Functions Formulas and Notes



Linear Functions


These are functions in the form \displaystyle y=mx+c.
m is the gradient. c is the y-intercept.

Example
\displaystyle f(x)=3x (c=0: the graph cuts the y-axis at 0; the gradient is 3)

x -2 -1 0 1 2
f(x) -6 -3 0 3 6



Example
\displaystyle f(x)=2x+5 (the graph cuts the y-axis at 5; the gradient is 2). A positive gradient produces a upward slope.

x -2 -1 0 1 2
f(x) 1 3 5 7 9



Example
\displaystyle f(x)=-2x+5 (the graph cuts the y-axis at 5; the gradient is -2). A negative gradient produces a downward slope.

x -2 -1 0 1 2
f(x) 9 7 5 3 1



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