Name ________________________________________ Date __________________ Class __________________
LESSON
6-3
Standard Form
Practice and Problem Solving: C
Write each equation in slope-intercept form. Then identify its intercepts.
1. 3x + 4y = 24
2. y = −5x + 10
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________________________________________
4. 9 x −
3. x − 7y − 15 = 0
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2
y = −4
3
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Graph each line. Rewrite the equation in standard form if necessary.
5. 6x + 5y = 30
6. 3( x + y ) − 2( x − y ) = 5(8 + 3 y )
Solve.
y −8
= 2 and y = 2 x + 6 have
x −1
identical lines as their graphs. Do you agree? Explain.
7. A student claims that the two equations
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8. A line is written in standard form Ax + By = 0, where A and B are not
both zero. Find the coordinates of the point that must lie on this line, no
matter what the choice of A and B.
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9. A line is written in standard form Ax + By = C, where A ≠ 0. Find the
x-coordinate of the point on the line at which y = 3.
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107
Success for English Learners
Practice and Problem Solving: C
x y
+ = 1; (8, 0) and (0, 6)
8 6
1. You cannot begin with slope-intercept
form because the y-intercept is not given.
1.
2. Subtracting a number is the same as
adding the opposite of the number. So,
subtracting a negative number is the
same as adding a positive number.
3. not standard; 2x + 2y = 8
x y
+
= 1; (2, 0) and (0, 10)
2 10
1
7
x
y
3.
x+−
y = 1 or
+
= 1;
15
15
15
15
−
7
15 ⎞
⎛
(15, 0) and ⎜ 0, −
7 ⎟⎠
⎝
9
1
x
y
⎛ 4 ⎞
+
= 1; ⎜ − , 0 ⎟ ;
4. − x + y = 1 or
4
4
6
6
⎝ 9 ⎠
−
9
and (0,6)
4. 6x − y = 11
5.
2.
3. Use the slope formula.
LESSON 6-3
Practice and Problem Solving: A/B
1. not standard; 3x − y = 0
2. not standard; 5x + y = −4
5. x + y = 7
6. 9x − y = −47
7.
6.
8.
7. y = 2x + 6 has a line as its graph.
y −8
= 2 has almost the same graph as
x −1
y = 2x + 6. The point (1, 8) is not a part of
its graph because the denominator of a
fraction cannot equal 0. The graph of
y −8
= 2 is a line with a hole in it at
x −1
(1, 8).
9. 200x − y = −50
10. x − 4y = −4
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522
Reading Strategies
8. (0, 0)
C − 3B
9.
A
1. x + 2y = 10
2. 2x − y = −4
3. x + y = 3
Practice and Problem Solving: Modified
1. standard
1
2. x − y = 8 or x − 2y = −16
2
6
4
3
0
−2
y
−3
−1
0
3
5
4. The equation x = 3 cannot be written in
standard form because there standard
form requires non-zero coefficients for
both the x and y terms by definition.
3. 2x − y = −2
4. point-slope
5. slope-intercept
6. standard
7.
x
x
0
1
2
3
y
0
2
4
6
Success for English Learners
1. No. Using the standard form x − y = −3,
−4 − 1 ≠ − 3.
2. Sample answers: (0, 3) and (−3, 0)
LESSON 6-4
Practice and Problem Solving: A/B
8.
x
0
1
2
3
y
5
4
3
2
1. y = 6x + 11
2. y = −5x − 1
3. y = 2x − 4
4. y = 6x − 1
5. y = x − 1
6. y = 2x
7. y = 3x − 1
8. y = 4x + 2
9. g(s) = 4000 + 0.05s
10. h(s) = 8000 + 0.15s
11. k(s) = 2000 + 0.3s
12.
Practice and Problem Solving: C
9. B; C; D; A
1. y = 2x − 3
2. 3x + 20y = 1
3. y = 2x − 20
4. y = 4x + 5
10. It is not the correct standard form. To
convert to standard form, you would need
to multiply both sides by 2 and then
subtract 3x from each side, so the correct
standard form of the given equation
should be −3x + 2y = 6.
5. y = 12x − 12
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