MS Algebra A-F-IF-7 – Ch. 6.1cSolving Word Problems by WritingEquations in Slope-Intercept Form

Mr. Deyo

Solving Word Problems by Writing Equations in Slope-Intercept Form

A 3,000 lb. mass is approaching your head at 40 ft/sec.

By the end of the period, I will solve word problems by writing and solving equations in slope-intercept form.

I will demonstrate this by completing Four-Square Notes and by solving problems in a pair/group activity.

Learning Target

Title: 6.1c Solve Word Problems with the Slope-Intercept Form Date:

Home Work 1-2-3: 1) Class 4-Square Notes Put In Binder?

2) Section 6.1 Pg. 327-328 3) Section ______

TxtBk.Prob. #42,43,44,45,47,49 Notes Copied on blank sheet Solved and Put in Binder? of paper in Binder?

Table of ContentsDate Description Date Due

Storm Check (Think, Write, Discuss, Report)

Questions on which to ponder and answer:1. How are the two images similar?

2. How are they different?

3. How can these two images be related to math?

A 3,000 lb. mass is approaching your head at 40 ft/sec.

1) Slope

2) y-intercept

3) Slope-Intercept Form

4) Point-Slope Form

Vocabulary

DAY 3 and/or DAY 4

1. Review the word

Friendly Definition

Physical Representation

2. Show how the word works

Synonyms/antonym

Word Problems

Related words/phrases

Example/non-example

Friendly DefinitionSketch

Wordwork Sentence

DAY 2

1. Review word

Friendly Definition

Physical Representation

2. Draw a sketch

DAY 5

1. Review the word

Friendly definition

Physical Representation

3. Write a sentence

at least 2 rich words (1 action)

correct spelling

correct punctuation

correct subject/predicate agreement

clear and clean writing

DAY 1

1. Use Visuals

2. Introduce the word

Friendly Definition

Physical Representation

3. Use Cognates

4. Write friendly definition

5. Physical Representation

Word List1.2.3.4.

For use with pages xxx–xxxDaily Warm-Up Exercises

Bill borrowed $75 from his parents.

He is paying back $5 per week.

Write an equation that models this situation.

For use with pages xxx–xxxDaily Warm-Up Exercises

Bill borrowed $75 from his parents.

He is paying back $5 per week.

Write an equation that models this situation.

ANSWER

y = 75 – 5x y = -5x + 75

y = mx + b

Notes: How To Get To Slope-Intercept Form

Slope-Intercept Form of a Linear Equation

m = slopeb = y-intercept

Step 1) Make a table

Use the two points to calculate SLOPE (m)

x y

X1 Y1

X2 Y2

Step 2) Plug m and one point into y = mx + bSolve for b

(Y1) = m(X1) + b

Step 3) Write general formula with m and b

m = Y2 – Y1

X2 – X1

Problem A

A recording studio charges musicians an initial fee of $50 to

record an album. Studio time costs an additional $35 per hour.

RECORDING

STUDIOSolve a multi-step problem

Write an equation that gives the total cost of an album as a function of studio time (in hours).

Find the total cost of recording

an album that takes 10 hours of studio time.

C = total cost T = number of hoursm = $35 per hour b = $50 initial cost

y = mx + b

Problem A

A recording studio charges musicians an initial fee of $50 to

record an album. Studio time costs an additional $35 per hour.

RECORDING

STUDIOSolve a multi-step problem

Write an equation that gives the total cost of an album as a function of studio time (in hours).

Find the total cost of recording

an album that takes 10 hours of studio time.

C = 35T + 50

C = total cost T = number of hoursm = $35 per hour b = $50 initial cost y = mx + b

C = 35T + 50C = 35(10) + 50C = 350 + 50

C = $400

y = mx + b

ANSWER

Problem B

In Problem A, suppose the recording studio raises its initial

fee to $75 and charges $40 per hour for studio time.

WHAT IF?

Write an equation that gives the total cost of an album as a function of studio time (in hours).

Find the total cost of recording

an album that takes 10 hours of studio time.

Problem B

In Problem A, suppose the recording studio raises its initial

fee to $75 and charges $40 per hour for studio time.

WHAT IF?

Write an equation that gives the total cost of an album as a function of studio time (in hours).

Find the total cost of recording

an album that takes 10 hours of studio time.

ANSWER

C = 40T + 75

y = mx + b

C = 40T + 75C = 40(10) + 75C = 400 + 75

C = $475

Vocabulary Check

1. In the equation y = mx + b, the value of m is the _____________ of the graph of the equation.

y-intercept

standard form

slope

conditional statement

slope-intercept form

parallel

2. In the equation y = mx + b, the value of b is the _____________ of the graph of the equation.

Two lines are _________________ if their slopes are equal.3.

Vocabulary Check

1. In the equation y = mx + b, the value of m is the _____________ of the graph of the equation. ANSWER

slope

ANSWER

y-intercept

y-intercept

standard form

slope

conditional statement

slope-intercept form

parallel

2. In the equation y = mx + b, the value of b is the _____________ of the graph of the equation.

Two lines are _________________ if their slopes are equal.3.

ANSWER

parallel

Skills Check #1

Find the slope of the line that passes through the points.

(4, 5) and (2, 3) (0, 0) and (-1, 2)

Skills Check #1

Find the slope of the line that passes through the points.

1

(4, 5) and (2, 3)

ANSWER

(0, 0) and (-1, 2)

3-52-4

= -2-2

= -2

ANSWER

2-0-1-0

= 2-1

=

Identify the slope (m) and y-intercept (b) of the line with the given equation.

Skills Check #2

6–4

3x=y

52

=y – 2–x

Identify the slope (m) and y-intercept (b) of the line with the given equation.

Skills Check #2

6–4

3x=y

52

=y – 2–x

43

ANSWER

, b = –6m =5-2

ANSWER

, b = –2m =

Storm Check (Think, Write, Discuss, Report)

If you are given two points, how can you create a linear equation that is in slope-intercept form?

(2-3 sentences)

When given two points, I can create a linear

equation in slope-intercept form by _______________

_______________________________________________

______________________________________________

______________________________________________.

By the end of the period, I will solve word problems by writing and solving equations in slope-intercept form.

I will demonstrate this by completing Four-Square Notes and by solving problems in a pair/group activity.

Learning Target

Title: 6.1c Solve Word Problems with the Slope-Intercept Form Date:

Home Work 1-2-3: 1) Class 4-Square Notes Put In Binder?

2) Section 6.1 Pg. 327-328 3) Section ______

TxtBk.Prob. #42,43,44,45,47,49 Notes Copied on blank sheet Solved and Put in Binder? of paper in Binder?

Table of ContentsDate Description Date Due

Ticket OUT. Find the slope or y-intercept given a point

Find the value of m or b if the given line passes through the given point.

(8, -4)y = 2x + b

Ticket OUT. Find the slope or y-intercept given a point

Find the value of m or b if the given line passes through the given point.

Substitute the coordinates of the given point into the equation and solve for b.

mx b+=y

SOLUTION

(8, -4)y = 2x + b

-4 = 2(8) + b

-4 = 16 + b

-20 = b