Transcript Linear_Equations_Review

Bellwork

Take Chapter 3 Review worksheet from
front of classroom, begin working the
problems
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Mrs. Motlow Classroom Procedures
Obtaining Help:
C3B4ME
1. If you need
help, ask a
classmate.
2. If not helped, ask
another classmate.
3. If still not helped, ask
the 3rd and final
classmate.
4. If still in need of help,
raise your hand.
5. I will come to your desk to
provide assistance or ask
you to come to my desk.
6. After being helped,
quietly return to your
seat.
If it is a common question, let
me know so we can share the
answer with the class.
Chapter 2 Refresh
-4(p+2) + 8 = 2(p – 1) – 7p + 15
-4p - 8 + 8 = 2p – 2 – 7p + 15
-4p + 0 = -5p +13
+5p
p = 13
-4(13+2)+8 = 2(13 -1) -7(13) + 15
-60 + 8 = 24 - 91 + 15
-52= -52
Distribute
Combine like terms
Solve for p
Check
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Amazing Race Review
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Linear Equations – Process Section

Standard Form of a Line
Ax + By = C
A & B are integers, both not equal to 0,

Non-Linear Equation may have xy, 1/x or x2
6. xy = 6 , is this linear?
7. 2x + 3y + 7 = 3, is this linear?, standard form
2x + 3y = 3 – 7
2x + 3y = -4
Graphing Using Intercepts
Intercept, where line crosses an Axis
 At that point, the other variable is = zero

Y Intercept where X = 0
 X Intercept where Y = 0

4. Find the x-intercept of x – 2y = 9.
x – 2(0) = 9
x=9
Graph the equation x – 4y = 2
X Intercept where Y = 0
x=2
 Y Intercept where X = 0
-4y = 2 .
y = 2/(-4)
y = -1/2

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Slope
• Slope RISE/RUN
M=10
M=2
• Higher the Value of Slope
• Steeper the Incline
• Approaching Vertical
M=1
M=1/2
Slope
• Slope RISE/RUN
M=10
M=2
• Higher the Value of Slope
• Steeper the Incline
• Approaching Vertical
• Lower the Value of Slope
• Flatter the incline
• Approaching Horizontal
M=1
M=1/2
M=1/10
Slope
• Positive Slope
▫M>0
▫ Rises from left to right
• Negative Slope
▫M<0
▫ Falls from left to right
• Zero Slope
▫0
▫ Horizontal
• Undefined Slope
▫ 1/0
▫ Vertical
M>0
M=0
M<0
M = 1/0
Undefined
Lines you should know
2x + y =8
x=4
y = -x
y=x
x+y=5
y=-4
9. Graph y = –1/2x.
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Slope
m= rise
run
m=
Y2 –Y1
X2 –X1
A(x1, y1)Y
10. What is the slope of the line through (1, 9)
and (-3, 16)?
B(x2, y2)
X
m=
16 - 9
7
-3 -1
-3
Rate of Change
11. In 2005, there were 12,000 students at
Beacon High. In 2010, there were
12,250. What is the rate of change in the
number of students?
a. 250/yr
b. 50/yr
c. 42/yr
d. 200/yr
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Direct Variation
13. If y varies directly as
x and y = 3 when x = 10,
Find x when y = 8.

If y varies directly
with x


Equation y = k x
k is constant of
variation

When Graphed, k is
same as m (slope) y = 10 x
Y = kx
3 = k(10)
3/10 = k
8 = 10 x
8/10 = x
Direct Variation

If y varies directly
with x


Equation y = k x
k is constant of
variation
4. If a shark can swim 27
miles in 9 hours, how many
miles will it swim in 12
hours?
Y = kx
27= k(9)
3= k
 When Graphed, k is
same as m (slope)
y=3x
y = 3(12)
Y = 36 miles
Direct Variation

If y varies directly
with x


Equation y = k x
k is constant of
variation
A driver’s distance varies
directly as the amount of time
traveled. After 6 hours, a
driver had traveled 390 miles.
How far had the driver
traveled after 4 hours?
Y = kx
390= k(6)
390/6 = k
 When Graphed, k is
65 = k
same as m (slope)
y = 65 x
y = 65(4)
Y = 260 miles
The number of seats in each row of a theater form an arithmetic
sequence,
8
14
20
26
?
Common
Difference = +6
nth term = a1+(n-1)d
14, How many seats are in the 12th row?
a12 term = 8+(12-1)6
a12= 8 + (11) 6 = 74
15. Which formula can be used to find the
number of seats in any given row?
an = 8+(n-1)6 = 8 + 6n – 6 = 6n + 2