Warm-Up Linear Functions - Edgenuity Inc.

Warm-Up

Linear Functions

Lesson Objectives

By the end of this lesson, you should be able to:

? Determine if a

? Represent a

is linear.

relationship numerically, algebraically, and

graphically.

W

2K

Words to Know

Write the letter of the definition next to the matching word as you work through

the lesson. You may use the glossary to help you.

_____ linear function

A. the point on a graph at which the graph

crosses the ?-axis

_____ point-slope form

B. the slope-intercept form of a linear equation

is given by ? = ?? + ?, where ? is the slope

and b is the ?-intercept

_____ slope-intercept form

C. the point-slope form of a linear equation is

given by ? ? ?1 = ?(? ? ?1 ), where (?1 , ?1 )

is a point on the line and m is the slope

_____ standard form of a

D. a function that can be written in the form

? ? = ?? + ?, where ? and ? are real

numbers; consists of a set of ordered pairs

all lying on the same line

linear equation

_____ ?-intercept

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E. the form ?? + ?? = ?, where ?, ?, and ? are

real numbers such that ? and ? are not both

zero, ? is positive if it is not zero, and the

greatest common factor of ?, ?, and ? is 1

1

Instruction

?

Linear Functions

Lesson

Question

Slide

3

Graphing Functions from Slope-Intercept Form

Graph ? = 2? + 3.

Connect the points to draw the graph.

y

? is the coefficient of ?.

4

? = 2, which we can write as ? =

.

x

?4

?=

4

Remember that the ?-intercept is a point,

so it has coordinates (

,

?4

).

Find the other points by using the slope.

You can go up 2, over to the right 1. You can also go down 2 and 1 to the left.

Standard Form of Linear Equation

Standard form of a linear equation

?? + ?? = ?,

where ?, ?, and ? are real numbers such that ? and ? are not both zero, ? is

if it is not zero, and the greatest common factor of ?, ?, and ?

is

.

Write the equation ?2? + ? = ?3 in standard form.

Multiply the equation through by ?1:

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2? ? ? =

2

Instruction

Linear Functions

Slide

5

Point-Slope Form of Linear Equation

Point-slope form of a linear equation

? ? 5 = 2(? ? 1)

?=2

? ? ?1 = ?(? ? ?1),

where (?1, ?1) is a

on the

Point: (

line and m is the

,

)

.

Write the equation in slope-intercept form.

??5=2 ??1

? ? 5 = 2? ? 2

+ 5

+5

Distribute.

Add 5 to both sides of the equation.

?=

The equations ? ? 5 = 2 ? ? 1 and ? = 2? + 3 are equivalent equations. That

means that if we graphed them, we would get the same exact

10

.

Modeling a Linear Relationship

Movie Tickets

Child: $6

Total Revenue: $1,500

Adult: $9

? = # of child tickets

? = # of adult tickets

6? +

=

You could also change this equation to slope-intercept form to graph it, to look at

the intercepts of the equation.

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3

Instruction

Linear Functions

Slide

12

Modeling a Linear Relationship

Example: Write a linear function to model the following situation:

An airplane is 30,000 ft. in the air and descending 1,000 ft. for each mile it travels.

��Descending�� means it��s going

.

Write the equation.

?=

Or, as a function

?(?) = 30,000 ? 1,000?

The question is: How far away from the airport does the airplane have to start to

descend to land safely? To answer that, we need to find the ?-intercept.

Plug in

for ?.

0 = 30,000 ? 1,000?

1,000? =

?=

The plane needs to start to descend 30

land safely.

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from the airport in order to

4

Summary

?

Linear Functions

Lesson

Question

How do you represent linear relationships?

Answer

Slide

2

Review: Key Concepts

Linear relationships can be written in one of the following forms.

Slope-intercept form: ? = ?? + ?

? is the

, ? is the ?-intercept

form of a linear equation: ?? + ?? = ? ,

? and ? are not both 0, ? is positive if it is not 0, and ?, ?, and ? have no

common factors.

Point-slope form: ? ? ?1 = ?(? ? ?1 )

? is the slope, (?1, , ?1 ) is a

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on the line

5

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