Linear and Non-Linear Functions y = 2x + 1 y = 𝟔 𝒙 8th Grade Math Presented by Mr. Laws

CCSS Standard 8.F.3 - Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. 8.F.4 – Find slope: Construct a function to model a linear relationship between two quantities.

Essential Question How do I define a linear function, and how do I identify examples of functions that are not linear?

What is a Linear or Non-Linear Function? A linear function is a specific function when graphed, will form a straight line on a coordinate plane. A non-linear function is a specific function when graphed, will not form a straight line on a coordinate plane. A linear function can be represented by a graph, a equation, or a function table.

Linear Function (Graph) A linear function graph is a set of order pairs (x,y) when plotted will form a straight line on a coordinate plane. y x y x y x y x Since these graphs displays a straight line, these are linear graphs.

Non-Linear Function (Graph) A non – linear function graph do not display a straight line. y x y x y x y x Non-Linear Graphs

A Linear Equations y = mx + b y = 1 2 x – 6 y = 2x + 1 y = 3x y = 1 A linear equation is an equation when graphed on a coordinate plane, will form a straight line. It is based on a math formula called slope intercept form (SIF): slope y = mx + b input output y- intercept Examples: y = 1 2 x – 6 y = 2x + 1 y = 3x y = 1 y = 𝑥 6 y = -x – 1 y = - 3 4 x – 5 y = -x y = -7

Non-Linear Equations Examples: y = 𝟔 𝒙 y = 2x2 + 1 y = 8x2 + 1x y = 4x Non – Linear equations are equations when graphed, will not form a straight line. Non – Linear equations do not match slope intercept form (y=mx+b). Examples: y = 𝟔 𝒙 y = 2x2 + 1 y = 8x2 + 1x y = 4x

Linear Function Table X Y Linear Function tables are functions tables when graphed on a coordinate plane, will form a straight line. For it to be a linear function, both the x-value and y- value must have a constant rate of change. + 2 + 1 The x-value has a constant rate of change of plus 1. X 1 2 3 4 5 Y 6 8 10 The y-value has a constant rate of change of plus 2. Since both x and y value have a constant rate of change, this is an linear function table. Constant rate of change = 𝐶ℎ𝑎𝑛𝑔𝑒𝑠 𝑜𝑓 𝑦 𝐶ℎ𝑎𝑛𝑔𝑒𝑠 𝑜𝑓 𝑥

Non-Linear Function Tables Non - Linear Function tables are functions tables that do not have a constant rate change in either the x-value or y-value or both. + 1 + 1 + 1 + 1 The x-value has a constant rate of change of plus 1. X 1 2 3 4 5 Y 8 12 20 The y-value does not have a constant rate of change. This function table is non-linear. + 1 + 5 +4 + 8

Summary Can you answer the essential question? Do you have any questions on what you have learned? Will you be able to write a summary based on the lesson?