Post on 01-Apr-2015
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Warm UpTuesday 11/9/10 We will graph linear equations using
intercepts.
Simplify each expression:
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a. 8x(x − 3) −10(x + 2)
b. 2x(x − 5) − 3(x + 4)
c. 3x(x − 2) − 5(x − 2)
d. 7x(x − 2) − 6(x + 3)
Warm UpWednesday 11/10/10 We will graph linear equations
using intercepts.
Solve each equation:
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a. 2
9x − 3 = 4
b. 3
5x − 8 =10
c. 2
7x −10 =12
Today’s Objective
•To be able to find the x and y intercepts of an equation and use them to draw a quick graph.
The Intercepts
y-Intercept = 6
x-Intercept = 2
The intercepts are
where the line crosses
the axis.
Intercepts: Find the x and y intercepts then graph the line
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4x + 5y = −20x intercept y = 0Substitute 0 in for y then solve for x
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4x + 5(0) = −20
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4x + 0 = −20
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4x = −20
x = −5
(−5, 0)
y intercept x = 0Substitute 0 in for x then solve for y
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4(0) + 5y = −20
0 + 5y = −20
5y = −20
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y = −4
(0, − 4)
Graph of equation
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4x + 5y = −20
Next graph the x intercept x = -5 at the point (-5,0)
First graph the y intercept y = -4 at the point (0,-4)
Finally connect the points to form a line
Intercepts: Find the x and y intercepts then graph the line
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3y = 2x − 24x intercept y = 0Substitute 0 in for y then solve for x
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3(0) = 2x − 24
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0 = 2x − 24
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24 = 2x
x =12
(12, 0)
y intercept x = 0Substitute 0 in for x then solve for y
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3y = 2(0) − 24
3y = 0 − 24
3y = −24
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y = −8
(0,−8)
Graph of equation
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3y = 2x − 24
Next graph the x intercept x = 12 at the point (12,0) (change scale count by 2s)
First graph the y intercept y = -8 at the point (0,-8)
Finally connect the points to form a line
Compare the 2 graphs3x+ y = 6
(1,3)
(0,6) (2,0)
(-1,9)
3x+ y = 6
x-intercept = 2y-intercept = 6
Find the intercepts and graph
3x + 4y = 12
Finding the x-intercept 3x + 4y = 12 3x + 4(0) = 12 3x + 0 = 12 3x = 12 x = 4
Finding the y-intercept 3x + 4y = 12 3(0) + 4y = 12 0 + 4y = 12 4y = 12 y = 3
The graph of 3x + 4y = 12
x-intercept = 4y-intercept = 3
Find the intercepts and graph
y = 4x - 4
You try this one.
Finding the x-intercept y = 4x - 4 0 = 4x - 4 0 + 4 = 4x -4 + 4 4 = 4x 1 = x
Finding the y-intercept y = 4x - 4 y = 4(0) - 4 y = -4
The graph of y = 4x - 4
x-intercept = 1
y-intercept = -4
What is the x-intercept of3x – 4y = 24?
1. (3, 0)
2. (8, 0)
3. (0, -4)
4. (0, -6)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30 31 32
What is the y-intercept of-x + 2y = 8?
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30 31 32
1. (-1, 0)
2. (-8, 0)
3. (0, 2)
4. (0, 4)
What is the y-intercept ofx = 3?
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30 31 32
1. (3, 0)
2. (-3, 0)
3. (0, 3)
4. None
Word Problem• You make and sell decorative bows. You sell
small bows for $3 and large bows for $5. You want to earn $60 per week. This situation can be modeled by 3x + 5y = 60 where x is the number of small bows and y is the number of large bows.
• Find the intercepts of the graph.• Graph the equation• Give 3 possible solutions
Finding the y-intercept 3x + 5y = 60 3(0) + 5y = 60 5y = 60 y = 12 (0, 12)
Finding the x-intercept 3x + 5y = 60 3x + 5(0) = 60 3x = 60 x = 20
(20, 0)
Graph of the Equation
Small Bows Sold
Three Possible Solutions
Small Bows Sold
0 small, 12 large0 small, 12 large
10 small, 6 large10 small, 6 large
20 small, 0 large20 small, 0 large
Word Problem• You borrow $1800 from your parents. To repay your debt, you give them $150 per month.
Your debt d (in dollars) is given by the function: d = 150t -1800 where t represents time in (months) • Find the intercepts of the graph of the function and
state what they represent.
• Graph the equation and identify its domain and range.
Finding the t-intercept d = 150t - 1800
Set d = 0 0 = 150t – 1800 1800 = 150t
12 = t
In 12 months the debt = 0
Finding the d-intercept d = 150t - 1800
Set t = 0 d = 150(0) - 1800 d = - 1800
The debt is -$1800 when time is 0.
Graph the function d = 150t -1800
Put time (t) on the x axisPut time (t) on the x axis
Put
deb
t (d)
on
the
y ax
isP
ut d
ebt (
d) o
n th
e y
axis
Graph of the function d = 150t -1800
deb
t (d)
in d
olla
rs d
ebt (
d) in
dol
lars
time (t) in months time (t) in months
(12, 0) (12, 0)
Identify the domain and range
deb
t (d)
in d
olla
rs d
ebt (
d) in
dol
lars
time (t) in months time (t) in months
Domain:
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0 ≤ t ≤12
Range:
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−1800 ≤ d ≤ 0
Guided Practice Pgs. 225 – 228
Examples 1 – 5