1. Solving Word Problems by Writing Equations in Slope-Intercept Form
MS Algebra A-F-IF-7 – Ch. 6.2 Solving Word Problems by Writing Equations in Slope-Intercept Form
Mr. Deyo
Solving Word Problems by Writing Equations in Slope-Intercept Form

2. Title: 6.2 Apply Slope-Intercept Form to Solve Word Problems
Date:
Learning Target
By the end of the period, I will apply the slope formula and the slope-intercept form to write equations and solve word 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 6.2 Pg ) Section ______
TxtBk.Prob. #28,33,37-43 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. Vocabulary Slope y-intercept Data Pair 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. Find the total cost after 9 mo.
Problem A
GYM MEMBERSHIP
Solve a multi-step problem
Your gym membership costs $33 per month after an initial membership fee. You paid a total of $228 after 6 months.
Write an equation that gives the total cost as a function of the length of your gym membership (in months) y = mx + b
What is the membership fee?
Find the total cost after 9 mo.
C = total cost N = number of mo.
m = $33 per mo b = membership fee

8. Problem A
SOLUTION
GYM MEMBERSHIP
Solve a multi-step problem
Your gym membership costs $33 per month after an initial membership fee. You paid a total of $228 after 6 months.
Write an equation that gives the total cost as a function of the length of your gym membership (in months) y = mx + b
What is the membership fee?
228 = 33(6) + b
228 = b
30 = b
Find the total cost after 9 mo.
y = mx + b
C = 33N + 30
C = 33(9) + 30
C =
C = $327
C = 33N b
C = total cost N = number of mo.
m = $33 per mo b = membership fee

9. Problem B
SOLUTION
GYM MEMBERSHIP
Solve a multi-step problem
A gym charges $35 per month after an initial membership fee. A member has paid a total of $250 after 6 months.
Write an equation that gives the total cost as a function of the length of your gym membership (in months) y = mx + b
What is the membership fee?
Find the total cost after 10 mo.
C = total cost N = number of mo.
m = $35 per mo b = membership fee

10. Problem B
SOLUTION
GYM MEMBERSHIP
Solve a multi-step problem
A gym charges $35 per month after an initial membership fee. A member has paid a total of $250 after 6 months.
Write an equation that gives the total cost as a function of the length of your gym membership (in months) y = mx + b
What is the membership fee?
250 = 35(6) + b
250 = b
40 = b
Find the total cost after 10 mo.
y = mx + b
C = 35N + 40
C = 35(10) + 40
C =
C = $390
C = 35N b
C = total cost N = number of mo.
m = $33 per mo b = membership fee

11. 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.

12. 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.

13. 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

14. Step 1: Find the slope between 2 points
Problem A
BMX RACING
Step 2: Find the value of b using m and 1 point
Given 2 data points
Step 3: Write general y = mx + b equation
In Bicycle Moto Cross (BMX) racing, racers purchase a one year membership to a track. They also pay an entry fee for each race at that track. One racer paid a total of $125 after 5 races. A second racer paid a total of $170 after 8 races. Q1) What is the entry fee (m) per race? Q2) How much does the track membership (b) cost?
Step 1:
m =
Step 2: R C
General Equation:
C = total cost R = number of races
m = entry fee/race b = yr. membership fee 14

15. C = 15R + 50 y = mx + b 170 = 15(8) + b 170 = 120 + b 50 = b 8 170 5
Step 1: Find the slope between 2 points
Problem A
SOLUTION
BMX RACING
Step 2: Find the value of b using m and 1 point
Given 2 data points
Step 3: Write general y = mx + b equation
In Bicycle Moto Cross (BMX) racing, racers purchase a one year membership to a track. They also pay an entry fee for each race at that track. One racer paid a total of $125 after 5 races. A second racer paid a total of $170 after 8 races. Q1) What is the entry fee (m) per race? Q2) How much does the track membership (b) cost?
Step 1:
y = mx + b
170 = 15(8) + b
170 = b
50 = b
m =
Step 2: R C 8
170 5
125
8-5 45 3 = = 15
Q1)
Q2)
C = mR b
General Equation:
C = 15R + 50
C = total cost R = number of races
m = entry fee/race b = yr. membership fee 15

16. y = mx + b R C C = mR + b m = Problem B
Step 1: Find the slope between 2 points
Problem B
BMX RACING
Step 2: Find the value of b using m and 1 point
Given 2 data points
Step 3: Write general y = mx + b equation
In Bicycle Moto Cross (BMX) racing, racers purchase a one year membership to a track. They also pay an entry fee for each race at that track. One racer paid a total of $76 after 3 races. Another racer paid a total of $124 after 7 races. Q1) What is the entry fee (m) per race? Q2) How much does the track membership (b) cost?
Step 1:
y = mx + b
Step 2:
m = R C
C = mR b
General Equation:
C = total cost R = number of races
m = entry fee/race b = yr. membership fee 16

17. C = 12R + 40 y = mx + b 124 = 12(7) + b 124 = 84 + b 40 = b 7 124 3 76
Step 1: Find the slope between 2 points
Problem B
SOLUTION
BMX RACING
Step 2: Find the value of b using m and 1 point
Given 2 data points
Step 3: Write general y = mx + b equation
In Bicycle Moto Cross (BMX) racing, racers purchase a one year membership to a track. They also pay an entry fee for each race at that track. One racer paid a total of $76 after 3 races. Another racer paid a total of $124 after 7 races. Q1) What is the entry fee (m) per race? Q2) How much does the track membership (b) cost?
Step 1:
y = mx + b
124 = 12(7) + b
124 = 84 + b
40 = b
124 – 76
m =
Step 2: R C 7
124 3 76
7 – 3 48 4 = = 12
Q1)
Q2)
C = mR b
General Equation:
C = 12R + 40
C = total cost R = number of races
m = entry fee/race b = yr. membership fee 17

18. 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 _______________
_______________________________________________
______________________________________________
______________________________________________.

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

20. Title: 6.2 Apply Slope-Intercept Form to Solve Word Problems
Date:
Learning Target
By the end of the period, I will apply the slope formula and the slope-intercept form to write equations and solve word problems.
I will demonstrate this by completing Four-Square Notes and by solving problems in a pair/group activity.

21. Home Work 1-2-3: 1) Class 4-Square Notes Put In Binder?
2) Section 6.2 Pg ) Section ______
TxtBk.Prob. #28,33,37-43 ALL Notes Copied on blank sheet Solved and Put in Binder? of paper in Binder?
Table of Contents
Date Description Date Due

22. 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 2: Find the value of b using
m and 1 point
Step 3: Write general y = mx + b equation
Turn to your partner and share your answer. Please use correct answer.
Partner B, please share what Partner A told you.

23. y = -2x + 7 -2 m = = = -1 = -2(4) + b -1 = -8 + b 7 = b -1 - 5 -6
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 2: Find the value of b using
m and 1 point
Step 3: Write general y = mx + b equation
Turn to your partner and share your answer. Please use correct answer.
Partner B, please share what Partner A told you.
y = -2x + 7
-1 = -2(4) + b
-1 = -8 + b
7 = b