1. Rule of the Linear Function

2. A Rule is a standard to follow in order to get the desired outcome.
In math, it is the equation one follows for the input that gives you the output Example: y = -3x + 2 or f(x) = x² - 9 x y x
f(x)

4. There are several types of functions
1) Linear Function - highest exponent of variables is 1
Example y = ¾ x + 6
Graph is a STRAIGHT line
2) Quadratic Function - highest exponent of variables is 2
Example y = 3x² - 4
3) Reciprocal Function – the variable x is in the denominator
Example y = ⅟x
4) Exponential Function – a number is raised to a variable exponent
Example y = 4ⁿ

5. Which equation shows a linear function?
y = 4x² + 8
y = x(x + 1)
y = x + 1 x
y = -6x – 2
y = 4 x
y = 2x³ - 7
y = ½ x + 9
y = x² - 5

6. Linear Functions The slope between any two points is the same Example:
How do you find slope from a table?
1) Pick any two points
2) Find change in y over change in x x y -3
-11 -1 -7 1 3 5

7. How to find the “RULE” of Linear Functions
From a Graph
1) Find the slope(m) using rise over run
2) Find ‘b’ – the y-intercept – where the
graph crosses the y-axis
3) Write the Rule
Substitute m and b into y = mx + b

8. How to find the “RULE” of Linear Functionsx y -3
-11 -1 -7 1 3 5
B) From a table
We want the rule to be y = mx + b
What do we need to find?
1) Find the slope
a) Pick any two points
b) Find Change in y over Change in x
c) Substitute m into y=mx+b
2) Find b
a) Pick any ordered pair
b) Substitute the x- and y- values
into y = mx + b
c) Solve for b
3) Write the rule

9. More Examples x y -2 -5 -1 2 3 4 7 6 11 x y -4 -10 -1 2 8 5 17 26 x-1 2 3 4 7 6 11 x y -4
-10 -1 2 8 5 17 26 x
f(x) -2 -3 1 2 5 4 6 x y -4 1 -2 2 3 4 5 x
f(x) -9 -5 -7 11 -3 19 -2 x y -2 -5 -4 2 -3 4 6 -1 x y -3 -6 -2 -1 2 6 1 10 x
f(x) -2 -5 3 -3 8 -1 13 1 18