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Every element of the input value is associated with one unique element of the output.
Linear function always forms a straight line.
For every x-input there is a y-output.
Each time y changes, x is either constant, decreasing or increasing.
An equation means two expressions are equal.
A function only outputs a value.
LINEAR FUNCTION FORMULA
Components of a linear function
f(x) = mx + b
dependent variable
input
slope
y = f(x) = mx + b)
independent variable
y-intercept
LINEAR FUNCTION FORMULA
Explanation of the linear function format
1)
slope
m =
1
1
y - y = change y
x - x = change x
y = mx + b
y - b = mx + b - b
y - b = mx
x x
y - b = m
x
2)
y-intercept
y = mx + b
when x = 0
y = m(0) + b
y = 0 + b
y = y-intercept = b
P (x, y)
(0, b) = y-intercept
y - b
x
(a, 0) = x-intercept
P (x , y )
1
1
Linear Function Formula
Explanation and example of linear function
Equation Table
y
f(x) = mx + b
x
input association output
y = mx + b is the same as F(x) = mx + b, except functions emphasizes:
-
A function means for every input there is one output.
-
They have x (dependent) and y (independent) variables.
-
These variable form a relationship.
-
Each output is related to one or more inputs.​
f(x) = 1 x + 3
3
Equation Table
f(x) = 1x/3 + 3
x
1(0)/ 3 + 3
1(-9)/3 + 3
1(3)/3 + 3
1(-6)/3 + 3
input association output
y
3
0
4
1
0
-9
3
-6
Function example:
y = x + 3
1
3
1
3
f(x) = x + 3
if x = -6
1
3
f(-6) = x + 3
1
3
f(-6) = (-6) + 3
-6
3
f(-6) = + 3
f(-6) = -2 + 3
f(-6) = 1
6
(3, 4)
6
4
(0, 3)
4
2
2
-2
-2
-8
-10
(-9, 0)
-6
-4
(-6, 1)
m
(x - )
x
1
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