Lesson 3: Linear Relations May 13, 2011

All linear relations can be expressed in the form: WHERE m is the ___slope_________ and b is the ____y-intercept____________.

Since relations can be expressed in many ways, it is important to be able to identify the key components and characteristics that make a relation linear. 1. Equations: An equation that represents a linear relation will be written (or can be expressed) in the form y= mx + b. *It is important to note that the x has an exponent of 1.

2. Graphs: When graphed, all linear relations will form a continuous straight line. 3. Tables of Values: In a table of values, the difference in value between consecutive dependent (y-axis) values/terms is called the first difference. All linear relations will have first differences that are constant (equal to each other). Another way of saying this is to say that all linear relations have a constant rate of change. (The independent values must increase or decrease by a constant value.)

Example 1: Are the following linear equations Example 1: Are the following linear equations? If so, rewrite them in the form y= mx + b. if not, explain why they are not linear. a) 3y = 4x – 6 Linear: b) y = 7x2 + 4 Quadratic c) 5x = y + 21 Linear: d) y = 6 Linear

e) 8y = 5x3 – 4 Cubic f) y = 5(4x – 6) Linear: Linear: g) x = 0 + 3y

Example 2: Which of the following lines can be described as linear? C and A are linear B is quadratic D is exponential

Example 3: Calculate the first differences for the following Example 3: Calculate the first differences for the following. Is the relation linear? Why or why not? x y 15 4 23 8 31 12 39 16 47 20 55

n 2 4 6 8 10 12 C 20 30 42