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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
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