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 .

65

65

Standard FormStandard FormALGEBRA 1 LESSON 6-3ALGEBRA 1 LESSON 6-3

6-3

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

6-3

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

6-3

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

6-3

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

6-3

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.

ALGEBRA 1 LESSON 6-3ALGEBRA 1 LESSON 6-3

Standard FormStandard Form

6-3

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.

ALGEBRA 1 LESSON 6-3ALGEBRA 1 LESSON 6-3

Standard FormStandard Form

6-3

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 –

ALGEBRA 1 LESSON 6-3ALGEBRA 1 LESSON 6-3

Standard FormStandard Form

6-3

y = x + 1045

46.

y = x + 367

45

59

53

ALGEBRA 1 LESSON 6-3ALGEBRA 1 LESSON 6-3

Standard FormStandard Form

6-3

53. y = – x – 8

54. y = x –

1611

19

23

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

ALGEBRA 1 LESSON 6-3ALGEBRA 1 LESSON 6-3

Standard FormStandard Form

6-3

1 36 1 12