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MS Algebra A-F-IF-7 – Ch. 6.3bSolving Real World Problems with the

Point-Slope FormMr. Deyo

Solving Problems by Writing Equations in Point-Slope Form

By the end of the period, I will apply the point-slope form to write equations and solve real world problems.

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

Learning Target

Title: 6.3b Apply Point-Slope Form to Solve Real World Problems Date:

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

2) Section 6.3 Pg. 345-346 3) Section ______

TxtBk.Prob.#45-49 ALL 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?

For use with pages xxx–xxxDaily Warm-Up Exercises

A golf course charges an yearly membership fee of $800 and

a greens fee of $8 for each round of golf play that year.

One year you spent $920.

How many rounds of golf did you play that year?

Step 1: Find the slope between 2 points

Step 2: Find the value of b using m and 1 point

Step 3: Write general y = mx + b equation

Rounds Costs

0 $800

1 $808

?? $920

For use with pages xxx–xxxDaily Warm-Up Exercises

A golf course charges an yearly membership fee of $800 and

a greens fee of $8 for each round of golf play that year.

One year you spent $920.

How many rounds of golf did you play that year?

Step 1: Find the slope between 2 points

Step 2: Find the value of b using m and 1 point

Step 3: Write general y = mx + b equation

Rounds Costs

0 $800

1 $808

?? $920

m =

y = mx + b(920) = (8)x + 800

920 = 8x + 800120 = 8x

800 = 8(0) + b800 = 0 + b

800 = b

808–8001 - 0

= 8 = 81

ANSWER

Step 3

Step 1

Step 2

x = 15

1) Slope

2) y-intercept

3) Data Pair

4) Slope-Intercept Form

5) 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.

Notes: How To Get To Point-Slope Form

Step 1) Plug m and one point into

y – Y1 = m(x – X1)

Step 2) Solve for y (if you want slope-intercept form)

x y

X1 Y1

Solve a multi-step problemProblem A

You have color flyers printed to advertise your band, _______________.

You pay $225 for the first 1000 flyers plus $80 for every 1000 extra flyers.

ADVERTISING

A) Write an equation that gives the total cost (in dollars) of the flyers as a function of the number (in thousands) of flyers that you buy.

B) Find the cost of 9000 flyers.

Solve a multi-step problemProblem A

STEP 1 Identify the rate of change and a data pair. Let C be the total

cost (in dollars) and F be the number of flyers (in thousands).

STEP 2 Write an equation using point-slope form. Rewrite the equation in slope-intercept form so that the total cost is a function of the number of flyers.

Rate of change, m: $80 per 1 thousand extra flyersData pair ( F1, C1 ) : 1 thousand flyers, $225

SOLUTION

=C1–C F1–Fm )(

=C +80F 145

The cost of 9000 stickers is $865.

Write point-slope form.

Substitute 80 for m, 1 for F1, and 225 for C1.

Solve for C.

=–C 1–F80 )(225

=–C 80–F80225

STEP 3 Find the cost of 9000 stickers.

C = 80F + 145C = 80 (9) + 145 C = 720 + 145C = $865

ANSWER

Problem B

Suppose a second company charges $250 for the first 1000 flyers. The

cost of each additional 1000 flyers is $60.

WHAT IF?Solve a multi-step

problem

ADVERTISING

A) Write an equation that gives the total cost (in dollars) of the flyers as a function of the number (in thousands) of flyers ordered.

B) Find the cost of 9000 flyers. Which company charges less for 9000 flyers?

Problem B

Suppose a second company charges $250 for the first 1000 flyers. The

cost of each additional 1000 flyers is $60.

WHAT IF?

The 2nd company

charges less.

Solve a multi-step

problem

ADVERTISING

A) Write an equation that gives the total cost (in dollars) of the flyers as a function of the number (in thousands) of flyers ordered.

B) Find the cost of 9000 flyers. Which company charges less for 9000 flyers?

ANSWER

ANSWER

C = 60F + 190C = 60(9) + 190C = 540 + 190

C = $730

C – C1 = M (F – F1) C – 250 = 60 (F – 1)C – 250 = 60F – 60

C = 60F + 190

Storm Check (Think, Write, Discuss, Report)

If you are given the slope and one point, how can you create a linear equation that is in point-slope form?

(2-3 sentences)

When given the slope and one point, I can create a

linear equation in point-slope form by _____________

_______________________________________________

_______________________________________________

______________________________________________.

By the end of the period, I will apply the point-slope form to write equations and solve real world problems.

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

Learning Target

Title: 6.3b Apply Point-Slope Form to Solve Problems Date:

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

2) Section 6.3 Pg. 345-346 3) Section ______

TxtBk.Prob.#45-49 ALL Notes Copied on blank sheet Solved and Put in Binder? of paper in Binder?

Table of ContentsDate Description Date Due

Notes: How To Get To Point-Slope FormStep 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 – Y1 = m(x – X1)

Step 3) Solve for y (if you want slope-intercept form)

m = Y2 – Y1

X2 – X1

Write a real-world linear

model from a tableProblem A

The table shows the cost of visiting a horse ranch for one day and night for different numbers of people. Can the situation be modeled by a linear equation? Explain. If possible, write an equation that gives the cost as a function of the number of people in the group.

HORSE RANCH

Number of People 4

Cost (dollars)

6 8 10 12

250 350 450 550 650

STEP 1 STEP 2 C – C1 = M(P – P1)m =

Write a real-world linear

model from a tableProblem A

Find the rate of change for consecutive data pairs in the table.

The table shows the cost of visiting a horse ranch for one day and night for different numbers of people. Can the situation be modeled by a linear equation? Explain. If possible, write an equation that gives the cost as a function of the number of people in the group.

HORSE RANCH

Number of People 4

Cost (dollars)

6 8 10 12

250 350 450 550 650

STEP 1

SOLUTION

450–550

8–10= 50,

550–650

10–12= 50

m = 50

C – C1 = M(P – P1)C – 250 = 50(P – 4)C – 250 = 50P – 200

C = 50P + 50Because the cost increases at a constant rate of $50 per person, the situation can be modeled by a linear equation.

Use point-slope form to write the equation. Let Cbe the cost (in dollars) and p be the number of people. Use the data pair (4, 250).

STEP 2

Problem B

The table shows the cost of sending a single piece of first class mail for different weights. Can the situation be modeled by a linear equation? Explain. If possible, write an equation that gives the cost of sending a piece of first class mail as a function of its weight.

MAILING COSTS

Weight (ounces) 1

Cost (dollars)

4 5 10 12

0.39 1.11 1.35 2.55 3.03

C – C1 = M(W – W1)m =Step 1) Step 2)

Problem B

The table shows the cost of sending a single piece of first class mail for different weights. Can the situation be modeled by a linear equation? Explain. If possible, write an equation that gives the cost of sending a piece of first class mail as a function of its weight.

MAILING COSTS

Weight (ounces) 1

Cost (dollars)

4 5 10 12

0.39 1.11 1.35 2.55 3.03

ANSWER Yes, because the cost increases at a constant rate of $.24 per ounce; C = 0.24W + 0.15

C – C1 = M (W – W1)C – 0.39 = 0.24(W – 1)C – 0.39 = 0.24W – 0.24

C = 0.24W + 0.15

m = 1.35 – 1.115 – 4

m = 0.24 / 1

m = 0.24

Step 1) Step 2)

Storm Check (Think, Write, Discuss, Report)

If you are given a table of data points, how can you determine if you can use a linear equation to model the situation?

(2-3 sentences)

When given a table of data points, I can determine if I

can use a linear equation to model the situation by

_______________________________________________

_______________________________________________

______________________________________________.

1) Slope

2) y-intercept

3) Data Pair

4) Slope-Intercept Form

5) Point-Slope Form

Vocabulary

By the end of the period, I will apply thepoint-slope form to write equations and solve real world problems.

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

Learning Target

Title: 6.3b Apply Point-Slope Form to Solve Problems Date:

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

2) Section 6.3 Pg. 345-346 3) Section ______

TxtBk.Prob.#45-49 ALL Notes Copied on blank sheet Solved and Put in Binder? of paper in Binder?

Table of ContentsDate Description Date Due

Ticket OUT.

Write an equation of the line that passes

through the points (1, 5) and (4, –1).Step 1: Find the slope between 2 points x y

Step 2a: Plug m and 1st point intoPoint-Slope Form

Step 2b: Plug m and the 2nd point into thePoint-Slope Form

Ticket OUT.

Write an equation of the line that passes

through the points (1, 5) and (4, –1).Step 1: Find the slope between 2 points x y

4 -1

1 5

y – y1 = m(x – x1)

y – 5 = -2(x – 1)

Step 2a: Plug m and 1st point intoPoint-Slope Form

Step 2b: Plug m and the 2nd point into thePoint-Slope Form

y – y2 = m(x – x2)

y + 1 = -2(x – 4)

m = -1 - 5

4 - 1=

-6

3= -2