1. Mr. Deyo Solving Problems by Writing Equations in Point-Slope Form
MS Algebra A-F-IF-7 – Ch. 6.3b Solving Real World Problems with the Point-Slope Form
Mr. Deyo
Solving Problems by Writing Equations in Point-Slope Form

2. By the end of the period, I will apply the
Title: 6.3b Apply Point-Slope Form to Solve Real World Problems
Date:
Learning Target
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.

3. Home Work 1-2-3: 1) Class 4-Square Notes Put In Binder?
2) Section 6.3 Pg ) Section ______
TxtBk.Prob.#45-49 ALL Notes Copied on blank sheet Solved and Put in Binder? of paper in Binder?
Table of Contents
Date Description Date Due

4. Storm Check (Think, Write, Discuss, Report) Questions on which to ponder and answer:
How are the two images similar?
How are they different?
How can these two images be related to math?
IMAGE 1
IMAGE 2

5. Daily Warm-Up Exercises
Step 1: Find the slope between 2 points
Daily Warm-Up Exercises
Step 2: Find the value of b using m and 1 point
For use with pages xxx–xxx
Step 3: Write general y = mx + b equation
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?
Rounds
Costs
$800 1
$808 ??
$920

6. Daily Warm-Up Exercises
Step 1: Find the slope between 2 points
Daily Warm-Up Exercises
Step 2: Find the value of b using m and 1 point
For use with pages xxx–xxx
Step 3: Write general y = mx + b equation
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
808–800 8 8
m = = =
Rounds
Costs
$800 1
$808 ??
$920
1 - 0 1
Step 2
800 = 8(0) + b
800 = 0 + b
800 = b
Step 3
y = mx + b
(920) = (8)x + 800
920 = 8x + 800
120 = 8x
ANSWER
x = 15

7. Vocabulary Slope y-intercept Data Pair Slope-Intercept Form
Point-Slope Form

8. Vocabulary Acquisition
Friendly Definition
Sketch
Wordwork
Sentence
DAY 2
1. Review word
Friendly Definition
Physical Representation
2. Draw a sketch
DAY 1
Use Visuals
Introduce the word
Friendly Definition
Physical Representation
Use Cognates
Write friendly definition
Word List
Vocabulary Acquisition
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
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

9. How To Get To Point-Slope Form
Notes:
Given
One
Point
&
SLOPE
Step 1) Plug m and one point into
y – Y1 = m(x – X1) x y X1 Y1
Step 2) Solve for y (if you want slope-intercept form)

10. B) Find the cost of 9000 flyers.
Problem A
ADVERTISING
Solve a multi-step problem
You have color flyers printed to advertise your band, _______________. You pay $225 for the first 1000 flyers plus $80 for every 1000 extra flyers.
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.

11. = C + 80F 145 = C1 – C F1 F m ) ( = – C 1 F 80 ) ( 225 = – C 80 F 225
Problem A
SOLUTION
Solve a multi-step problem
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).
Rate of change, m: $80 per 1 thousand extra flyers
Data pair ( F1, C1 ) : 1 thousand flyers, $225
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. = C1 – C F1 F m ) (
Write point-slope form. = – C 1 F 80 ) (
Substitute 80 for m, 1 for F1, and 225 for C1.
225 = – C 80 F
225
Solve for C. = C +
80F
145
C = 80F + 145
C = 80 (9) + 145
C =
C = $865
STEP 3
Find the cost of 9000 stickers.
ANSWER
The cost of 9000 stickers is $865.

12. Problem B ADVERTISING WHAT IF?
Solve a multi-step problem
WHAT IF?
Suppose a second company charges $250 for the first 1000 flyers. The cost of each additional 1000 flyers is $60.
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?

13. C = 60F + 190 C = $730 C – C1 = M (F – F1) C – 250 = 60 (F – 1)
Problem B
ADVERTISING
Solve a multi-step problem
WHAT IF?
Suppose a second company charges $250 for the first 1000 flyers. The cost of each additional 1000 flyers is $60.
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?
C – C1 = M (F – F1)
C – 250 = 60 (F – 1)
C – 250 = 60F – 60
C = 60F + 190
C = 60F + 190
C = 60(9) + 190
C =
C = $730
ANSWER
ANSWER
The 2nd company charges less.

14. 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 _____________
_______________________________________________
______________________________________________.

15. By the end of the period, I will apply the
Title: 6.3b Apply Point-Slope Form to Solve Problems
Date:
Learning Target
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.

16. Home Work 1-2-3: 1) Class 4-Square Notes Put In Binder?
2) Section 6.3 Pg ) Section ______
TxtBk.Prob.#45-49 ALL Notes Copied on blank sheet Solved and Put in Binder? of paper in Binder?
Table of Contents
Date Description Date Due

17. m = How To Get To Point-Slope Form Y2 – Y1 X2 – X1 X1 Y1 X2 Y2 Notes:
Given
Two
Points x y X1 Y1 X2 Y2
Step 1) Make a table
Use the two points to calculate SLOPE (m)
Y2 – Y1
m =
X2 – X1
Step 2) Plug m and one point into
y – Y1 = m(x – X1)
Step 3) Solve for y (if you want slope-intercept form)

18. m = HORSE RANCH Problem A
Write a real-world linear model from a table
HORSE RANCH
Problem 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.
Number of People 4 6 8 10 12
Cost (dollars)
250
350
450
550
650
STEP 1
m =
STEP 2
C – C1 = M(P – P1)

19. C = 50P + 50 m = 50 C – C1 = M(P – P1) C – 250 = 50(P – 4)
Write a real-world linear model from a table
HORSE RANCH
Problem A
SOLUTION
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.
Number of People 4 6 8 10 12
Cost (dollars)
250
350
450
550
650
STEP 1
Find the rate of change for consecutive data pairs in the table.
STEP 2
Use point-slope form to write the equation. Let C be the cost (in dollars) and p be the number of people. Use the data pair (4, 250).
450 –
550 8 10 =
50,
C – C1 = M(P – P1)
C – 250 = 50(P – 4)
C – 250 = 50P – 200
C = 50P + 50
650 –
550 = 50 12 – 10
m = 50
Because the cost increases at a constant rate of $50 per person, the situation can be modeled by a linear equation.

20. C – C1 = M(W – W1) m = Problem B MAILING COSTS
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.
Weight (ounces) 1
Cost (dollars) 4 5 10 12
0.39
1.11
1.35
2.55
3.03
m =
C – C1 = M(W – W1)
Step 1)
Step 2)

21. C = 0.24W + 0.15 m = 0.24 C – C1 = M (W – W1) C – 0.39 = 0.24(W – 1)
Problem B
MAILING COSTS
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.
Weight (ounces) 1
Cost (dollars) 4 5 10 12
0.39
1.11
1.35
2.55
3.03
C – C1 = M (W – W1)
C – 0.39 = 0.24(W – 1)
C – 0.39 = 0.24W – 0.24
C = 0.24W
m = 1.35 – 1.11
5 – 4
m = 0.24 / 1
m = 0.24
Step 1)
Step 2)
Yes, because the cost increases at a constant rate of $.24 per ounce; C = 0.24W
ANSWER

22. 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
_______________________________________________
______________________________________________.

23. Vocabulary Slope y-intercept Data Pair Slope-Intercept Form
Point-Slope Form

24. By the end of the period, I will apply the
Title: 6.3b Apply Point-Slope Form to Solve Problems
Date:
Learning Target
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.

25. Home Work 1-2-3: 1) Class 4-Square Notes Put In Binder?
2) Section 6.3 Pg ) Section ______
TxtBk.Prob.#45-49 ALL Notes Copied on blank sheet Solved and Put in Binder? of paper in Binder?
Table of Contents
Date Description Date Due

26. 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 into
Point-Slope Form
Step 2b: Plug m and the 2nd point into the
Point-Slope Form
Turn to your partner and share your answer. Please use correct answer.
Partner B, please share what Partner A told you.

27. -2 m = = = y – y1 = m(x – x1) y – 5 = -2(x – 1) y – y2 = m(x – x2)
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
-1 - 5 -6 -2
m = = =
4 - 1 3
Step 2a: Plug m and 1st point into
Point-Slope Form
Step 2b: Plug m and the 2nd point into the
Point-Slope Form
Turn to your partner and share your answer. Please use correct answer.
Partner B, please share what Partner A told you.
y – y1 = m(x – x1)
y – 5 = -2(x – 1)
y – y2 = m(x – x2)
y + 1 = -2(x – 4)