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Skills to know:
Write a system of equa5ons from a word problem. Solve a system of equa5ons using subs5tu5on. Solve a system of equa5ons using elimina5on.
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Solve the system of equa5ons: Slide 5
Solve the system of equa5ons: Slide 6
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Understand Systems of Inequali4es
Skills to know: Write a system of inequali5es from a word problem. Interpret graph of system of inequali5es (focus on the meaning of the doIed/solid line)
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a. Is the point (3,4) a solu5on to this system of inequali5es?
b. Is the point (-‐2,-‐2) a solu5on to this system of inequali5es?
c. Is the point (0,-‐2) a solu5on to this system of inequali5es?
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When y is -‐1, what values of x make this system of inequali5es true?
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Skills to know Meaning of slope and y-‐intercept from a table Graph a linear inequality Interpret slope from a word problem and equa5on in slope-‐intercept form Graph in standard form
Linear equa5ons and inequali5es
Slope-‐intercept form:
Find and explain the meaning of the
Slope –
Y-‐intercept -‐
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Find and explain the meaning of the
Slope –
Y-‐intercept -‐
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Your grandmother started a bank account for you when you were first born and con5nued. to add to it every month. The following equa5on can be used to determine the amount of money in your account at any given month.
y = 12.5m + 100
What is the slope and what does it mean in this situa5on?
What is the y-‐intercept and what does it mean in this situa5on?
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Graph this line in standard form:
3x + 4y = 12
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Graph this inequality:
y < -‐2x +5
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Skills to know: Write func5ons from a word problem. Add or subtract them.
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Skills to know: How to write recursive rules How to write explicit rule of sequences
Explicit rules:
Write an explicit rule and a recursive rule for this arithme5c sequence:
14, 11, 8, 5, …
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Write an explicit rule and a recursive rule for the cost of placing an order for n large pizzas.
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Skills to know: Frac5onal exponents
Exponents
D
E
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Skills to know: Interpolate answers from a graph and a given equa5on Interpret the real-‐world rela5onship between x and y on a scaIerplot Correla5on coefficient Residuals
The graph shows the distance you travel over a 6-‐hour period. The equa5on, y = 55x + 15 was wriIen for the line of best fit. At what distance would you be acer driving 20 hours?
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You are researching the prices of liquid crystal display (LCD) televisions. The scaIer plot shows the sizes and prices of several LCD televisions. The equa5on d = 25x – 400 models the line of best fit that you drew. Based on the informa5on given, what can you predict a 45-‐inch televisionwould cost?
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What is the rela5onship between the score on the Regents test and the number of hours studied?
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About where would the scaIer plot be on the correla5on line below? Es5mate the correla5on coefficient.
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About where would the scaIer plot be on the correla5on line below? Es5mate the correla5on coefficient.
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About where would the scaIer plot be on the correla5on line below? Es5mate the correla5on coefficient.
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About where would the scaIer plot be on the correla5on line below? Es5mate the correla5on coefficient.
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About where would the scaIer plot be on the correla5on line below? Es5mate the correla5on coefficient.
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About where would the scaIer plot be on the correla5on line below? Es5mate the correla5on coefficient.
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Answer to slide 3
(-‐1,-‐6)
Answer to slide 4
(-‐5,-‐1)
Answer to slide 5
No solu5on
Answer to slide 6
Same line Infinitely many solu5ons
Answer to slide 7
R = 34x
34x = 4x + 180 x = 6 Selling 6 bracelets will be the break-‐even point
Answer to slide 8
Let x = pens and y = pencils
x + y = 21 y + 3 = x
12 pens, 9 pencils
Answer to slide 9
20 scented 8 unscented
Answer to slide 10
$6
Answer to slide 12 a. b = pounds of blueberries s = pounds of strawberries
b.
€
4b + 3s ≤ 21b + s ≥ 3
c. d. yes
Answer to slide 13
€
12w +10c ≥110w + c ≤ 20
Answer to slide 14
a. Yes b. No c. No
Answer to slide 15
x > -‐3
Answer to slide 17
Slope = $1 for every 2 5ckets
Y-‐intercept = 0 You don’t have to pay any money if you aren’t buying any 5ckets
€
12
Answer to slide 18
Slope = 58 miles per hour
Y-‐intercept = 0 You started at the beginning, you haven’t gone any distance when you started the clock.
€
581
Answer to slide 19
Slope = 12.5 Your grandmother deposits $12.50 into your account every month
Y-‐intercept = 100 Your grandmother ini5ally deposited $100 to start the account.
Answer to slide 20
Answer to slide 21
Answer to slide 23 7. r(x) = 18x
8. c(x) = 30,000 + 4.5x
9. 13.5x – 30,000
10. $3000 loss
11. $172,500 profit
Answer to slide 24
Listeners: L(d) = d
Furniture store: f(d) = 5000 + d
Theater: g(d) = 2d
L(d) + f(d) + g(d) = 5000 + 4d
Answer to slide 28
Explicit Rule: 14 – (n – 1)3
Recursive Rule: f(1) = 14 f(n) = f(n-‐1) -‐ 3
Answer to slide 29
Answer to slide 32 A. 216
B. 32
C. 8
D. .
E. .
€
m4( )3
€
12
Answer to slide 34
1115 miles
Answer to slide 35
$725 (use the equa5on, not the graph)
Answer to slide 36
There is a posi5ve rela5onship between the score on the Regents test and the number of hours you study. As the number of hours studying increases, the score on the test increases.
Answer to slide 40
Answer to slide 41
Answer to slide 45
Answer to slide 46
Answer to slide 47
Answer to slide 48
Answer to slide 49
Answer to slide 50
