WEEK 12-EVALUATING-LINEAR-FUNCTIONS

Evaluating Linear Functions

Start

Objectives

Some Characteristics

Summary

Checking for Linearity

Linear Functions

Story

Story

Linear Functions

is the independent variable.

are the variables

x,y

m=2 b=-4

y=2x-4

f(x)=mx+b

Where:

Example 1: is a linear function,

mand b

are constants.

Here:

Definition: A linear function is in the form:

What is a Linear Function?

f(x)=3x-1

Example 2: Graph function defined on all of the real numbers.

Linear Functions can be visually represented on a graph.

Some Characteristics of Linear Functions

+1 +1 +1 +1

+2 +2 +2 +2

↺↺↺↺

↷↷↷↷

y=2x+4

Example: Linear Function increases 2 units in y for every increment of 1 in x.

Linear functions exhibit a constant rate of change. This means that for every increase in x, there is a proportional increase or decrease in y.

🗨️

Solution

a) Determine how much increases the price for each additional orange b) Plot the points on a cartesian plane.

Maria is planning to buy some oranges and found the following table of prices in the supermarket:

Taking Decisions at Supermarket

Checking for Linearity

It is a linear function

It is not a linear function

+1 +1 +1 +1

+1 +1 +1 +1

+1 +3 +5 +7

-1 -1 -1 -1

↺ ↺ ↺ ↺

↺ ↺ ↺ ↺

↷ ↷ ↷ ↷

↷ ↷ ↷ ↷

y=-x+3

Example 3: Determine if the function is a linear function or not. Graph it.

Example 2: Determine whether the values of the table belong to a linear function.

Let's see some examples:

🤔

a) Does given data follow a linear function? c) Plot points on a Cartesian Plane and if they are linear join them with a line.

You are a financial analyst and need to determine if a savings account can be modeled as a linear function base on the deposits per month made by a client.

Try it by Yourself

07:00

Click here to draw >

The solution will appear in 45 seconds

• {(-1,30),(1,15),(3,0)} -> Linear
• {(0,0),(1,1),(2,2)} -> Linear
• {(0,-500),(0,-400),(0,-300)} -> Linear
• {(0,0),(1,1),(2,8)} -> Nonlinear

{(0,0),(1,1),(2,8)}

{(0,-500),(0,-400),(0,-300)}

{(0,0),(1,1),(2,2)}

{(-1,30),(1,15),(3,0)}

Linear

Linear

Nonlinear

Linear

Link the type of function with the set of points.

Try it by yourself:

Summary: Functions

RAISE (SLOPE)

GRAPHIC

NONLINEAR

LINEAR

8TH-EVALUATING-LINEAR-FUNCTIONS-EN © 2024 by CASURID is licensed under CC BY-NC-ND 4.0

See you next time

Great job!

A journey soon begin through Social Science experiences!

Welcome 6th graders!

• Grid paper.
• Pencils of different colors.
• Eraser.
• A rule.
• A compass.
• A Protactor.
• A calculator.
• Geogebra installed on your phone/tablet/computer (or use online version).

MATERIAL

It is highly advised to have:

+1 +1 +1 +1

+169 +169 +169 +169

↺ ↺ ↺ ↺

↷ ↷ ↷ ↷

Deposits follow a linear pattern/function.

a)

b)

Step 4

Answer

Step 1

Step 2

Step 3

Solution

MA.8.F.1 Define, evaluate and compare functions. MA.8.F.1.2 "Given a function defined by a graph or an equation, determine whether the function is a linear function. Given an input-output table, determine whether it could represent a linear function." MA.K12.MTR.5.1 Use patterns and structure to help understand and connect mathematical concepts.

+1 +1 +1 +1

+550 +550 +550 +550

↺ ↺ ↺ ↺

↷ ↷ ↷ ↷

Orange prices raise $550 for each additional unit.

a)

b)

Step 4

Answer

Step 1

Step 2

Step 3

Solution