1. Standard form of a linear equation is Ax + By = C
Lesson 6.3
Standard form of a linear equation is Ax + By = C
Where A, B, and C are real numbers and A and B are not both zero.
X-intercept—is the x-coordinate of the point where a line crosses the x-axis.

2. Find the x- and y-intercepts of 2x + 5y = 6.
Standard Form
ALGEBRA 1 LESSON 6-3
Find the x- and y-intercepts of 2x + 5y = 6.
Step 1  To find the x-intercept, substitute 0 for y and
solve for x.
2x + 5y = x + 5(0) = x = x = 3
The x-intercept is 3.
Step 2  To find the y-intercept,
substitute 0 for x and
solve for y.
2x + 5y = 6
2(0) + 5y = 6
5y = 6
y =
The y-intercept is . 6 5
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3. You Try:
Find the x and y intercept of 4x – 9y = -12
Find x
4x – 9 (0) = -12
4x = -12
x = -3
Find y
4(0) -9 y = -12
-9y = -12
Y = 4/3 or 1 1/3

4. Graph 3x + 5y = 15 using intercepts.
Standard Form
ALGEBRA 1 LESSON 6-3
Graph 3x + 5y = 15 using intercepts.
Step 1  Find the intercepts.
3x + 5y = 15
3x + 5(0) = 15 Substitute 0 for y.
3x = 15 Solve for x.
x = 5
3(0) + 5y = 15 Substitute 0 for x.
5y = 15 Solve for y.
y = 3
Step 2  Plot (5, 0) and (0, 3).
Draw a line through the points.
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5. 0 • x + 1 • y = 4 Write in standard form. For all values of x, y = 4.
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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6. You try:
Graph:
Y = 5
Write in standard form:
0· x + 1· y = 5
For all values of x, y = 5
X = -4
1 · x + 0 · y = -4
For every y x = -4

7. Write y = x + 6 in standard form using integers.
ALGEBRA 1 LESSON 6-3
Write y = x + 6 in standard form using integers. 2 3
y = x + 6 2 3
3y = 3( x + 6 ) Multiply each side by 3.
3y = 2x Use the Distributive Property.
–2x + 3y = Subtract 2x from each side.
The equation in standard form is –2x + 3y = 18.
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8. You try:
Write y = -2/5 x + 1 in standard form using integers.
(-5) y = -5(-2/5x + 1)
-5y = -2x + -5
+2x +2x
2x + -5y =-5

9. Define: Let = the hours mowing lawns.
Standard Form
ALGEBRA 1 LESSON 6-3
Write an equation in standard form to find the number of hours you would need to work at each job to make a total of $130.
Define:  Let = the hours mowing lawns.
Let = the hours delivering newspapers. x y
Amount Paid per hour
Job
Mowing
lawns
$12
Delivering
newspapers
Relate: $12 per h   plus $5 per h equals   $130
mowing delivering $5
Write:  = x y
The equation standard form is 12x + 5y = 130.
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10. Standard Form pages 301–303 Exercises 1. 18; 9 2. 3; –9 3. –6; 30
ALGEBRA 1 LESSON 6-3
pages 301–303  Exercises
1. 18; 9
2. 3; –9
3. –6; 30
4. ; –3
5. – ; –
6. –8; 12
7. 6; 4
8. ; –2
9. –5; 4
10. B
11. C
12. A
13.
14.
15.
16.
17.
18.
19. horizontal
20. vertical
21. horizontal
22. vertical
23.
24.
3 2
9 2
3 2
4 7
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11. Standard Form 25. 26. 27. –3x + y = 1 28. 4x – y = 7 29. x – 2y = 6
ALGEBRA 1 LESSON 6-3
25.
26.
27. –3x + y = 1
28. 4x – y = 7
29. x – 2y = 6
30. –2x + 3y = 15
31. –3x – 4y = 16
32. –4x – 5y = 35
33. –14x + 4y = 1
34. 4x + 10y = 1
35. 3x + y = 0
36. a. Answers may vary.
Sample: x = no. of cars;
y = no. of vans or trucks
b. 5x + 6.5y = 800
37. a. Answers may vary.
Sample:
x = time walking;
y = time running
b. 3x + 8y = 15
38.
39.
40.
41.
42.
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12. Standard Form 47. a. 3x + 7y = 28 43. 51. y = – x – 3 b. 7 oz 44.
ALGEBRA 1 LESSON 6-3
47. a. 3x + 7y = 28
b. 7 oz
x y = 30
49.
50. 4 5
43.
44.
45.
51. y = – x – 3
52. y = x – 5 9 3
y = x + 10 4 5
46.
y = x + 3 6 7
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13. Sample: slope-intercept form when comparing the
Standard Form
ALGEBRA 1 LESSON 6-3
53. y = – x – 8
54. y = x – 16 11 1 9 2 3
55. Answers may vary.
Sample: slope-intercept
form when comparing the
steepness of two lines;
standard form when
making quick graphs
56. Answers may vary.
Sample: 0x + 0y = 0,
no linear equation exists.
57. –3x instead of 3x
58. y = 2
59. y = –2
60. x = 1
61. x = –2
62. a. 200s + 150a = 1200 b.
Answers may vary.
Sample:
s = $2.00, a = $5.33;
s = $3.00, a = $4.00;
s = $6.00, a = $0.00
s = $3.00 and
a = $4.00 because
they are whole dollar
amounts, and adults
pay more.
63. y = x + 4 5
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14. three of the following: 1 Supreme, 35 Prestige; [3] correct equation
Standard Form
ALGEBRA 1 LESSON 6-3
64.   square
65. a.
b. – ; –
c. Answers may vary.
Sample: The x- and
y-intercepts of 2x +
3y = 18 are 3 times
those of 2x + 3y = 6.
66. C
67. H
68. [2] y = x + 1;
x – 4y = –4
[1] correct slope-
intercept equation
69. [4] a. 48x + 56y = 2008 b.
c. Answers will include
three of the following:
1 Supreme, 35 Prestige;
8 Supreme, 29 Prestige;
15 Supreme, 23 Prestige;
22 Supreme, 17 Prestige;
29 Supreme, 11 Prestige;
36 Supreme, 5 Prestige
[3] correct equation
and graph
[2] wrong equation,
but a corresponding
correct graph
[1] Correct equation only
70. yes
71. no
72. no
73.
74.
75. 4
77. –0.5
78. –21 1 4 1 36 1 12 2 3 2 3
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