lesson 6.3 standard form of a linear equation is ax + by = c where a, b, and c are real numbers and...
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Lesson 6.3 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.
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 = 6
2x + 5(0) = 6
2x = 6
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 .
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Standard FormStandard FormALGEBRA 1 LESSON 6-3ALGEBRA 1 LESSON 6-3
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You Try:You Try:
Find the x and y intercept of 4x – 9y = -12
Find x4x – 9 (0) = -124x = -124 4x = -3
Find y4(0) -9 y = -12-9y = -12-9 -9Y = 4/3 or 1 1/3
Step 2 Plot (5, 0) and (0, 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
Graph 3x + 5y = 15 using intercepts.
Standard FormStandard Form
Draw a line through the points.
ALGEBRA 1 LESSON 6-3ALGEBRA 1 LESSON 6-3
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a. Graph y = 4 b. Graph x = –3.
Standard FormStandard Form
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.
ALGEBRA 1 LESSON 6-3ALGEBRA 1 LESSON 6-3
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You try:You try:
Graph:
Y = 5
Write in standard form:
0· x + 1· y = 5
For all values of x, y = 5
Graph:
X = -4
1 · x + 0 · y = -4
For every y x = -4
The equation in standard form is –2x + 3y = 18.
–2x + 3y = 18 Subtract 2x from each side.
y = x + 623
23
3y = 3( x + 6 ) Multiply each side by 3.
3y = 2x + 18 Use the Distributive Property.
Write y = x + 6 in standard form using integers.23
Standard FormStandard FormALGEBRA 1 LESSON 6-3ALGEBRA 1 LESSON 6-3
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You try: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
Define: Let = the hours mowing lawns.
Let = the hours delivering newspapers.
x
y
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.
Amount Paid per hour
Mowing lawns $12
Deliveringnewspapers $5 Relate: $12 per h plus $5 per h equals $130
mowing delivering
Write: 12 + 5 = 130x y
The equation standard form is 12x + 5y = 130.
Standard FormStandard FormALGEBRA 1 LESSON 6-3ALGEBRA 1 LESSON 6-3
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Job
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.
3 2 3
2
9 2
4 7
16.
17.
18.
19. horizontal
20. vertical
21. horizontal
22. vertical
23.
24.
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25.
26.
27. –3x + y = 128. 4x – y = 729. x – 2y = 630. –2x + 3y = 1531. –3x – 4y = 1632. –4x – 5y = 3533. –14x + 4y = 134. 4x + 10y = 135. 3x + y = 0
36. a. Answers may vary. Sample: x = no. of cars;y = no. of vans or trucks
b. 5x + 6.5y = 80037. a. Answers may vary.
Sample: x = time walking; y = time running
b. 3x + 8y = 1538.
39.
40.
41.
42.
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43.
44.
45.
47. a. 3x + 7y = 28b. 7 oz
48. 4.29x + 3.99y = 30
49.
50.
51. y = – x – 3
52. y = x –
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y = x + 1045
46.
y = x + 367
45
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53. y = – x – 8
54. y = x –
1611
19
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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 = 1200b.
Answers may vary. Sample: s = $2.00, a = $5.33; s = $3.00, a = $4.00; s = $6.00, a = $0.00s = $3.00 and a = $4.00 because they are whole dollar amounts, and adults pay more.
63. y = x + 435
66. C67. H
68. [2] y = x + 1;
x – 4y = –4[1] correct slope-
intercept equation69. [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
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.
23
23
14
[3] correct equation and graph
[2] wrong equation, but a corresponding correct graph
[1] Correct equation only70. yes71. no72. no
73.
74.75. 476. 2.2577. –0.578. –21
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