2.5B Create an Equation, Table and Graph

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2.5B Create an Equation, Table and Graph

In this lesson you will create an equation, table, and graph

from a verbal representation

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Slope-intercept form:y = mx + b

Slope(rate of change)

y-intercept(initial value)

y = -1.5x + 2

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Let’s ReviewLet’s ReviewA linear function has a constant rate of change

(slope) and an initial value (y-intercept).

y = 3x + 2

x y0 21 52 83 11

5 – 23

1 – 01

31

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Let’s ReviewCore Lesson

A wild animal park opens with 100 antelope and the population grows

by 5 antelope every year.y-interceptSlope

y = 100 + 5x

Example1:Create an equation, table, and graph from a verbal representation

Let’s ReviewCore Lesson

x (years) y (antelope)

0 1001 1052 1103 115

Y-intercept

51105 - 1001 – 0

y = + x100Slope = 5 1 =5 5

Example 1- continuedConstruct (write) a numeric representation from the verbal representation.

Let’s ReviewCore Lesson

Slope = 5y-intercept

y = + x 100

5

102

102

Example 1 continuedConstruct (write) a algebraic function from the graphic representation.

Example 2:Create an equation, table, and graph from a verbal representation.

Joan’s aunt agreed to loan Joan $500 to buy a used car as long as Joan pays back $50 per month.

Let’s ReviewCore LessonJoan’s Aunt agrees to loan Joan $500 to

buy a used car as long as Joan pays back $50

per month.

Slope “indicator”

slope = 50y-intercept = -500

y = 50x - 500

Let’s ReviewCore Lesson

x (months)

y (remaining debt)

0 -500

Joan’s Aunt agrees to loan Joan $500 to buy a used car as long as Joan pays

back $50 per month.

1 -4502 -4003 -350

-450 - -5001 - 0

y-intercept

50=

=1

slope

Let’s ReviewCore LessonJoan’s Aunt agrees to loan Joan $500 to buy a used car as long as Joan pays back $50 per month.

Let’s ReviewGuided PracticePractice Example 1:Linda begins the year with $200 in her bank account. Each month, she deposits $50. Create an equation, table, and graph from this verbal representation .

Let’s ReviewExtension ActivitiesPractice Example 2:A parachutist is 500 feet above the ground. After she opens her parachute, she falls at a constant rate of 25 feet per second.

Create the equation, table, and graph for the scenario.

Let’s ReviewGuided PracticePractice Example 3:Construct an algebraic equation using the graph provided below.

5

25

Let’s ReviewExtension Activities

Homework: Problems 1-9

Let’s ReviewExtension ActivitiesHomework Problem 1:Construct an algebraic equation for each of the given representations.

x y0 -115 -41

15 -10130 -191

Multiply x by 0.6 and add 7

a b

c

10

50

Let’s ReviewExtension ActivitiesHomework Problem 2:Write an algebraic equation for this scenario. Make a table to help before you write it.

Parking Lot Prices

Each hour . . . $1.50 Entrance fee . . . $3.00

Let’s ReviewQuick QuizHomework Problem 3

Jordan’s movie rental company charges a monthly fee of $5.00 plus an additional cost of $1.25 per movie rental. Which of these equations represents the total monthly cost (c) of renting (x) movies?

a) C = 1.25x + 5.00 b) C = 3.75x + 5.00 c) C = 5.00x + 1.25 d) C = 5.00x + 3.75

Let’s ReviewQuick Quiz

Homework Problem 4:Which is the graph of y = -3x + 5 ?

a

b

c

d

Let’s ReviewExtension ActivitiesHomework Problem 5

Match each equation to its table.y = -4x - 3 y = -3 + 4xy = -3x - 4

x y -4 8-2 2-1 -12 -10

x y -4 -19-2 -11-1 -72 5

x y -4 13-2 5-1 12 -11

Let’s ReviewQuick QuizHomework Problem 6

A restaurant charges $160 for a room and $10 per person for food and drinks. Which table is correct for this situation?

x y 0 $1503 $1806 $25010 $300

x y 0 $1603 $1706 $18010 $190

x y 1 $1603 $2106 $27010 $350

x y 0 $1603 $1906 $22010 $260

a b c d

Let’s ReviewQuick QuizHomework Problem 7 :

Another restaurant charges $150 for a room and $10 per person for food and drinks. Which is the correct graph?

a b c d

Let’s ReviewGuided PracticeHomework Problem 8:Thomas is 300 miles away from home. He drives 50 miles per hour.

Create an equation, table, and graph to represent this situation.

Let’s ReviewExtension ActivitiesHomework Problem 9: We had 15 inches of snow. It snowed at a rate of 5 inches per hour.

Create an equation, table, and graph for the scenario.