Rule of the Linear Function

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)

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

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

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

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

How to find the “RULE” of Linear Functions x 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

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