1. Solving Word Problems by Writing Equations in Slope-Intercept Form
MS Algebra A-F-IF-7 – Ch. 6.1c Solving Word Problems by Writing Equations 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.

2. Title: 6.1c Solve Word Problems with the Slope-Intercept Form
Date:
Learning Target
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.

3. Home Work 1-2-3: 1) Class 4-Square Notes Put In Binder?
2) Section 6.1 Pg ) 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 Contents
Date Description Date Due

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

5. Vocabulary
Slope
y-intercept
Slope-Intercept Form
Point-Slope Form

6. 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

7. Daily Warm-Up Exercises
For use with pages xxx–xxx
Bill borrowed $75 from his parents.
He is paying back $5 per week.
Write an equation that models this situation.

8. Daily Warm-Up Exercises
For use with pages xxx–xxx
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

9. Slope-Intercept Form of a Linear Equation
How To Get To Slope-Intercept Form
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 = mx + b
Solve for b
(Y1) = m(X1) + b
Step 3) Write general formula with m and b
y = mx + b
m = slope
b = y-intercept
Slope-Intercept Form of a Linear Equation

10. Problem A RECORDING STUDIO
Solve a multi-step problem
A recording studio charges musicians an initial fee of $50 to record an album. Studio time costs an additional $35 per hour.
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 hours
m = $35 per hour b = $50 initial cost
y = mx + b

11. C = $400 C = 35T + 50 Problem A ANSWER RECORDING STUDIO
Solve a multi-step problem
A recording studio charges musicians an initial fee of $50 to record an album. Studio time costs an additional $35 per hour.
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 hours
m = $35 per hour b = $50 initial cost
y = mx + b
C = 35T + 50
C = 35(10) + 50
C =
C = $400
C = 35T
y = mx + b

12. Problem B
WHAT IF?
In Problem A, suppose the recording studio raises its initial fee to $75 and charges $40 per hour for studio time.
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.

13. Problem B
ANSWER
WHAT IF?
In Problem A, suppose the recording studio raises its initial fee to $75 and charges $40 per hour for studio time.
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.
y = mx + b
C = 40T + 75
C = 40(10) + 75
C =
C = $475
C = 40T

14. Vocabulary Check y-intercept slope slope-intercept form standard form
conditional statement
parallel
In the equation y = mx + b, the value of m is the _____________ of the graph of the equation.
In the equation y = mx + b, the value of b is the _____________ of the graph of the equation. 3.
Two lines are _________________ if their slopes are equal.

15. parallel Vocabulary Check slope y-intercept y-intercept slope
slope-intercept form
standard form
conditional statement
parallel
ANSWER
slope
In the equation y = mx + b, the value of m is the _____________ of the graph of the equation.
ANSWER
y-intercept
In the equation y = mx + b, the value of b is the _____________ of the graph of the equation.
ANSWER
parallel 3.
Two lines are _________________ if their slopes are equal.

16. (4, 5) and (2, 3) (0, 0) and (-1, 2) Skills Check #1
Find the slope of the line that passes through the points.
(4, 5) and (2, 3)
(0, 0) and (-1, 2)

17. Skills Check #1
Find the slope of the line that passes through the points.
(4, 5) and (2, 3)
(0, 0) and (-1, 2)
ANSWER
ANSWER
3-5
2-4 -2 2 -1 = =
2-0
-1-0 1 = = -2

18. 6 – 4 3 x = y 5 2 = y – x Skills Check #2
Identify the slope (m) and y-intercept (b) of the line with the given equation. 6 – 4 3 x = y 5 2 = y – x

19. Skills Check #2
Identify the slope (m) and y-intercept (b) of the line with the given equation. 6 – 4 3 x = y 5 2 = y – x
ANSWER
ANSWER 4 3 5 -2
m =
, b = –6
m =
, b = –2

20. 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 _______________
_______________________________________________
______________________________________________
______________________________________________.

21. Title: 6.1c Solve Word Problems with the Slope-Intercept Form
Date:
Learning Target
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.

22. Home Work 1-2-3: 1) Class 4-Square Notes Put In Binder?
2) Section 6.1 Pg ) 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 Contents
Date Description Date Due

23. 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.
y = 2x + b
(8, -4)
Turn to your partner and share your answer. Please use correct answer.
Partner B, please share what Partner A told you.

24. Ticket OUT.
Find the slope or y-intercept given a point
SOLUTION
Find the value of m or b if the given line passes through the given point.
y = 2x + b
(8, -4) mx b + = y
Substitute the coordinates of the given point into the equation and solve for b.
-4 = 2(8) + b
Turn to your partner and share your answer. Please use correct answer.
Partner B, please share what Partner A told you.
-4 = 16 + b
-20 = b