Standard Form

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Standard Form
ALGEBRA 1 LESSON 6-3
(For help, go to Lessons 2-3 and 2-6.)
Solve each equation for y. 1. 3x y 5 2. y
2x 10 3. x y 6 4. 20x 4y 8 5.
9y 3x 1 6. 5y 2x 4 Clear each equation
of decimals. 7. 6.25x 8.5 7.75 8. 0.4 0.2x
5 9. 0.9 0.222x 1
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Standard Form
ALGEBRA 1 LESSON 6-3
Solutions
1. 3x y 5 2. y 2x 10 3x
3x y 5 3x y 2x 2x 10 2x
y 3x 5 y 2x 10 3. x y
6 4. 20x 4y 8 x 6 y
4y 20x 8 x 6 y y
y x 6 y 5x 2 5. 9y
3x 1 6. 5y 2x 4 9y 3x 1
5y 2x 4 y
y y x y
x
7. Multiply each term by 100 100(6.25x)100(8.5)
100(7.75) Simplify 625x 850
775 8. Multiply each term by 10 10(0.4)
10(0.2x) 10(5) Simplify 4 2x 50 9.
Multiply each term by 1000 1000(0.9)1000(0.222
x)1000(1) Simplify 900 222x 1000
20x 8 4
3x 1 9
1 9
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Standard Form
ALGEBRA 1 LESSON 6-3
Step 1  To find the x-intercept,
substitute 0 for y and solve for x. 2x
5y 6 2x 5(0) 6 2x 6
x 3
The x-intercept is 3.
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Standard Form
ALGEBRA 1 LESSON 6-3
Step 1  Find the intercepts.
3x 5y 15 3x 5(0)
15 Substitute 0 for y. 3x 15 Solve
for x. x 5 3x 5y 15
3(0) 5y 15 Substitute 0 for x.
5y 15 Solve for y. y 3
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Standard Form
ALGEBRA 1 LESSON 6-3
a. Graph y 4
b. Graph x 3.
0 x 1 y 4 Write in standard form. For
all values of x, y 4.
1 x 0 y 3 Write in standard form. For
all values of y, x 3.
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Standard Form
ALGEBRA 1 LESSON 6-3
2 3
Write y x 6 in standard form using
integers.
3y 2x 18 Use the Distributive Property.
2x 3y 18 Subtract 2x from each side.
The equation in standard form is 2x 3y 18.
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Standard Form
ALGEBRA 1 LESSON 6-3
Amount Paid per hour
Job
Mowing lawns
12
Delivering newspapers
Relate 12 per h   plus 5 per h
equals   130 mowing delivering
5
The equation standard form is 12x 5y 130.
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Standard Form
ALGEBRA 1 LESSON 6-3
x 4, y 12
horizontal
vertical
5 2
5x 2y 6 or 5x 2y 6
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Point-Slope Form and Writing Linear Equations
ALGEBRA 1 LESSON 6-4
(For help, go to Lessons 6-1 and 1-7.)
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Point-Slope Form and Writing Linear Equations
ALGEBRA 1 LESSON 6-4
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Point-Slope Form and Writing Linear Equations
ALGEBRA 1 LESSON 6-4
Graph the equation y 2 (x 1).
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Point-Slope Form and Writing Linear Equations
ALGEBRA 1 LESSON 6-4
y y1 m(x x1)
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Point-Slope Form and Writing Linear Equations
ALGEBRA 1 LESSON 6-4
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Point-Slope Form and Writing Linear Equations
ALGEBRA 1 LESSON 6-4
(continued)
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Point-Slope Form and Writing Linear Equations
ALGEBRA 1 LESSON 6-4
The relationship is linear. The rate of change
is 2.
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Point-Slope Form and Writing Linear Equations
ALGEBRA 1 LESSON 6-4
(continued)
Step 2 Use the slope 2 and a point (2,4) to write
an equation.
y y1 m(x x1) Use the point-slope form.
y 4 2(x 2) Substitute (2, 4) for (x1, y1)
and 2 for m.
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Point-Slope Form and Writing Linear Equations
ALGEBRA 1 LESSON 6-4
The relationship is not linear.
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Point-Slope Form and Writing Linear Equations
ALGEBRA 1 LESSON 6-4
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