Page 1Algebra I Unit 2 Linear Relationships

Chapter 4 Equations of Linear Functions

Lesson 4-1 Graphing Equations in Slope-Intercept Form

Objectives: I can write and graph linear equations in slope-intercept form.

I can model real-world data with equations in slope-intercept form.

CCSS: F.IF.7a, S.ID.7, MP.2, MP.8

Example 1: Write and graph an equation

Write an equation in slope-intercept form of the line with a slope of and a y-intercept of 1.Then graph the equation.

O

o

qD

y= mxtb

y=-3¥• 1L•

up%?gy;; start at

left 3( OID

Guided Practice 1: Write and graph an equationWrite an equation in slope-intercept form of the line with a slope of and a y-intercept of –8 .Then graph the equation.

Example 2: Graph linear equationsGraph

Guided Practice 2: Graph linear equations

Graph

-=D 0

y=mx+b

y=÷3x+-8

ifY= mxtb

-

× - × -4g = . x +8I

,I

, I,

Y=¥x -2

Example 3: Graph Linear Equations

Graph

Guided Practice 3: Graph Linear Equations

Graph

Standardized Test Example 4: Write an Equation in Slope-Intercept Form

Which of the following is an equation in slope-intercept form for theline shown in the graph?

A C

B D

Guided Practice 4: Write an Equation in Slope-Intercept Form

y =m×tB

y= 0×+1-

ii.::•

-2 = y=tz

: =P

Which of the following is an equation in slope-intercept form forthe line shown in the graph?

F H

G J

Real-World Example 5: Write and Graph a Linear Equation

The ideal maximum heart rate for a 25 yr old exercising to burn fat is 117 beats per minute. Forevery five yrs older than 25, that ideal rate drops three beats per minute.

a. Write a linear equation to find the ideal maximumheart rate for anyone over 25 who is exercising toburn fat.

b. Graph the equation.

c. Find the ideal maximum heart rate for a 55 yr old person exercising to burn fat.

•

'

0•w¥•@xx--1•

:y=¥×+1¥

"

53.lk#oomtrhruteFge%

0%5 123

.

55-25=30* ¥ !?I,I¥Eaa -

×

Guided Practice 5: Write and Graph a Linear Equation

The band boosters are selling sandwiches for $5 each. Theybought $1160 in ingredients.

a. Write an equation for the profit P made on nsandwiches.

b. Graph the equation.

c. Find the total profit if 1400 sandwiches are sold.

Lesson 4-2 Writing Equations in Slope-Intercept Form

Objectives: I can write an equation of a line in slope-intercept form given the slope andone point.I can write an equation of a line in slope-intercept form given two points.

CCSS: F.BF.1a, F.BF.1b, F.LE.2, MP.3, MP.6Example 1: Write an Equation Given the Slope and a Point

Write an equation of a line that passes through with a slope of .

&- , ,,§

' 2 3 45

-

.

--

:

-1150 go

Pz 5h - 1160•

.

a.

54400 ) - 1160 :$58@

Y=mxtB xy

- ↳ m

¥¥±¥¥I3D+B B=zyY⇒×€

Guided Practice 1: Write an Equation Given the Slope and a PointWrite an equation of a line that passes through the given point and has the given slope.

a. , slope 3

b. , slope –1

Example 2: Write an Equation Given Two PointsWrite an equation of the line that passes through each pair of points.

a. and

b. and

Guided Practice 2: Write an equation of the line that passes through each pair of points.

a. and

b. and

Real-World Example 3: Use Slope-Intercept Form

During one year, Malik’s cost for self-serve regular gasoline was $3.20 on the first of June and$3.42 on the first of July. Write a linear equation to predict Malik’s cost of gasoline the first ofany month during the year, using 1 to represent January.

× yor

Y=M×+By=z×t@5=3# + B

Bell5=-6+13

t 6+6

X Y m

-7=-1 ( 4) + BB= -3

Y=¥-7=-4 + B

+4 +4

× 's, xzyz 5=411 ) + B

5,1*2 =l2z=F 5-4+13

Y#4D- 4 -

y

xy 13=1

y=mxtB

33¥'s -67=-1'

¥j÷.gg?taBy=.#Xl 4 , Xz Yz

× y- 8=-4 (4) +13

12¥ = ¥=Il= . 4-

§,o=I!8+ B Axa

- l - 4 8=13 Y'

y=Fxt5,z5×¥os>g¥=÷

× "

o=±st⇒tB 0=45%+13B= -43

- ¥ - '

13

1€¥June- 3.20 → ( 6,35.⇒m=34I3jt=•2÷•zJuly -3.42 → (7,3-42) 3.20=-22 (6) t B

3.20=1.32+13 88

- 1.32- 1.32

Bet

Guided Practice 3: Use Slope-Intercept Form

In addition to his weekly salary, Ethan is paid $16 per delivery. Last week, he made 5 deliveries,and his total pay was $215. Write a linear equation to find Ethan’s total weekly pay T if he makesd deliveries.

Real-World Example 4: Predict from Slope-Intercept Form

On average, Malik uses 25 gallons of gasoline per month. He budgeted $100 for gasoline inOctober. Use the prediction equation in “Real-World Example 3” (above) to determine if Malikwill have to add to his budget. Explain.

Guided Practice 4: Predict from Slope-Intercept Form

Use the equation in “Guided Practice 3” to predict how much money Ethan will earn in a week ifhe makes 8 deliveries.

Lesson 4-3 Writing Equations in Point-Slope Form

Objectives: I can write equations of lines in point-slope form.

I can write linear equations in different forms.

CCSS: F.IF.2, F.LE.2, MP.2

o d-oy=MxtBM=l6 215=16 (5) + B

T= hed -1135

( 5,215 )215=80+13- so

-80

13=135

-D

← naff.

22Mt 1.88 4.08 ( 25 ) #102

C= -2240 ) + , .ggNO 102>100

C = 2.20 + 1. ss #4.08not enough $

F- 16 (8) +1351=128+135

= $263