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MS Algebra A-F-IF-7 – Ch. 6.1cSolving Word Problems by WritingEquations 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.
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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.
Learning Target
Title: 6.1c Solve Word Problems with the Slope-Intercept Form Date:
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Home Work 1-2-3: 1) Class 4-Square Notes Put In Binder?
2) Section 6.1 Pg. 327-328 3) 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 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?
A 3,000 lb. mass is approaching your head at 40 ft/sec.
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1) Slope
2) y-intercept
3) Slope-Intercept Form
4) 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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For use with pages xxx–xxxDaily Warm-Up Exercises
Bill borrowed $75 from his parents.
He is paying back $5 per week.
Write an equation that models this situation.
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For use with pages xxx–xxxDaily Warm-Up Exercises
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
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y = mx + b
Notes: How To Get To Slope-Intercept Form
Slope-Intercept Form of a Linear Equation
m = slopeb = y-intercept
Step 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 = mx + bSolve for b
(Y1) = m(X1) + b
Step 3) Write general formula with m and b
m = Y2 – Y1
X2 – X1
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Problem A
A recording studio charges musicians an initial fee of $50 to
record an album. Studio time costs an additional $35 per hour.
RECORDING
STUDIOSolve a multi-step problem
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 hoursm = $35 per hour b = $50 initial cost
y = mx + b
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Problem A
A recording studio charges musicians an initial fee of $50 to
record an album. Studio time costs an additional $35 per hour.
RECORDING
STUDIOSolve a multi-step problem
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 = 35T + 50
C = total cost T = number of hoursm = $35 per hour b = $50 initial cost y = mx + b
C = 35T + 50C = 35(10) + 50C = 350 + 50
C = $400
y = mx + b
ANSWER
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Problem B
In Problem A, suppose the recording studio raises its initial
fee to $75 and charges $40 per hour for studio time.
WHAT IF?
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.
![Page 13: MS Algebra A-F-IF-7 Ch. 6maestrodeyo.weebly.com/uploads/1/7/1/0/17102056/ms... · A recording studio charges musicians an initial fee of $50 to record an album. Studio time costs](https://reader036.vdocument.in/reader036/viewer/2022081523/5fcafe870df05559043519ea/html5/thumbnails/13.jpg)
Problem B
In Problem A, suppose the recording studio raises its initial
fee to $75 and charges $40 per hour for studio time.
WHAT IF?
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.
ANSWER
C = 40T + 75
y = mx + b
C = 40T + 75C = 40(10) + 75C = 400 + 75
C = $475
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Vocabulary Check
1. In the equation y = mx + b, the value of m is the _____________ of the graph of the equation.
y-intercept
standard form
slope
conditional statement
slope-intercept form
parallel
2. In the equation y = mx + b, the value of b is the _____________ of the graph of the equation.
Two lines are _________________ if their slopes are equal.3.
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Vocabulary Check
1. In the equation y = mx + b, the value of m is the _____________ of the graph of the equation. ANSWER
slope
ANSWER
y-intercept
y-intercept
standard form
slope
conditional statement
slope-intercept form
parallel
2. In the equation y = mx + b, the value of b is the _____________ of the graph of the equation.
Two lines are _________________ if their slopes are equal.3.
ANSWER
parallel
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Skills Check #1
Find the slope of the line that passes through the points.
(4, 5) and (2, 3) (0, 0) and (-1, 2)
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Skills Check #1
Find the slope of the line that passes through the points.
1
(4, 5) and (2, 3)
ANSWER
(0, 0) and (-1, 2)
3-52-4
= -2-2
= -2
ANSWER
2-0-1-0
= 2-1
=
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Identify the slope (m) and y-intercept (b) of the line with the given equation.
Skills Check #2
6–4
3x=y
52
=y – 2–x
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Identify the slope (m) and y-intercept (b) of the line with the given equation.
Skills Check #2
6–4
3x=y
52
=y – 2–x
43
ANSWER
, b = –6m =5-2
ANSWER
, b = –2m =
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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 _______________
_______________________________________________
______________________________________________
______________________________________________.
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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.
Learning Target
Title: 6.1c Solve Word Problems with the Slope-Intercept Form Date:
![Page 22: MS Algebra A-F-IF-7 Ch. 6maestrodeyo.weebly.com/uploads/1/7/1/0/17102056/ms... · A recording studio charges musicians an initial fee of $50 to record an album. Studio time costs](https://reader036.vdocument.in/reader036/viewer/2022081523/5fcafe870df05559043519ea/html5/thumbnails/22.jpg)
Home Work 1-2-3: 1) Class 4-Square Notes Put In Binder?
2) Section 6.1 Pg. 327-328 3) 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 ContentsDate Description Date Due
![Page 23: MS Algebra A-F-IF-7 Ch. 6maestrodeyo.weebly.com/uploads/1/7/1/0/17102056/ms... · A recording studio charges musicians an initial fee of $50 to record an album. Studio time costs](https://reader036.vdocument.in/reader036/viewer/2022081523/5fcafe870df05559043519ea/html5/thumbnails/23.jpg)
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.
(8, -4)y = 2x + b
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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.
Substitute the coordinates of the given point into the equation and solve for b.
mx b+=y
SOLUTION
(8, -4)y = 2x + b
-4 = 2(8) + b
-4 = 16 + b
-20 = b