ms algebra a-f-if-7 ch. 6helpmeteach.weebly.com/uploads/1/7/1/0/17102056/ms... · solving real...
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![Page 1: MS Algebra A-F-IF-7 Ch. 6helpmeteach.weebly.com/uploads/1/7/1/0/17102056/ms... · Solving Real World Problems with the Point-Slope Form Mr. Deyo Solving Problems by Writing Equations](https://reader036.vdocument.in/reader036/viewer/2022062604/5fc3ad053abd605e29147573/html5/thumbnails/1.jpg)
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
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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:
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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
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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?
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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
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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
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1) Slope
2) y-intercept
3) Data Pair
4) Slope-Intercept Form
5) Point-Slope Form
Vocabulary
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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.
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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
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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.
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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
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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?
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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
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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 _____________
_______________________________________________
_______________________________________________
______________________________________________.
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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:
![Page 16: MS Algebra A-F-IF-7 Ch. 6helpmeteach.weebly.com/uploads/1/7/1/0/17102056/ms... · Solving Real World Problems with the Point-Slope Form Mr. Deyo Solving Problems by Writing Equations](https://reader036.vdocument.in/reader036/viewer/2022062604/5fc3ad053abd605e29147573/html5/thumbnails/16.jpg)
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
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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
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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 =
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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
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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)
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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)
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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
_______________________________________________
_______________________________________________
______________________________________________.
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1) Slope
2) y-intercept
3) Data Pair
4) Slope-Intercept Form
5) Point-Slope Form
Vocabulary
![Page 24: MS Algebra A-F-IF-7 Ch. 6helpmeteach.weebly.com/uploads/1/7/1/0/17102056/ms... · Solving Real World Problems with the Point-Slope Form Mr. Deyo Solving Problems by Writing Equations](https://reader036.vdocument.in/reader036/viewer/2022062604/5fc3ad053abd605e29147573/html5/thumbnails/24.jpg)
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:
![Page 25: MS Algebra A-F-IF-7 Ch. 6helpmeteach.weebly.com/uploads/1/7/1/0/17102056/ms... · Solving Real World Problems with the Point-Slope Form Mr. Deyo Solving Problems by Writing Equations](https://reader036.vdocument.in/reader036/viewer/2022062604/5fc3ad053abd605e29147573/html5/thumbnails/25.jpg)
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
![Page 26: MS Algebra A-F-IF-7 Ch. 6helpmeteach.weebly.com/uploads/1/7/1/0/17102056/ms... · Solving Real World Problems with the Point-Slope Form Mr. Deyo Solving Problems by Writing Equations](https://reader036.vdocument.in/reader036/viewer/2022062604/5fc3ad053abd605e29147573/html5/thumbnails/26.jpg)
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
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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