Linear Functions Formulas and Notes

Linear Functions

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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