Fundamentals of, Statistics, Sullivan - Solutions, summaries, and outlines. 2022 updated

CD
Topics to Discuss
CD-1 Lines y2 − y1 4 − 2 2
6. Slope = = = = −2
x2 − x1 3 − 4 −1
1− 0 1
1. (a) Slope = =
2−0 2
(b) If x increases by 2 units, y will
increase by 1 unit.
1− 0 1
2. (a) Slope = =−
−2−0 2

(b) If x increases by 2 units, y will
decrease by 1 unit. y2 − y1 1− 3 −2 1
7. Slope = = = =−
x2 − x1 2 − (− 2) 4 2
1− 2 1
3. (a) Slope = =−
1 − (− 2) 3

(b) If x increases by 3 units, y will
decrease by 1 unit.

2 −1 1
4. (a) Slope = =
2 − (−1) 3

(b) If x increases by 3 units, y will
increase by 1 unit. y2 − y1 3 −1 2
8. Slope = = =
x2 − x1 2 − (− 1) 3
y2 − y1 0 − 3 −3
5. Slope = = =
x2 − x1 4 − 2 2




586

, CD-1 Lines


y2 − y1 −1 − (−1) 0 y2 − y1 2 − 0 2
9. Slope = = = =0 12. Slope = = = undefined.
x2 − x1 2 − (−3) 5 x2 − x1 2 − 2 0




13. P = (1, 2 ) ; m = 3
y −y 2−2 0
10. Slope = 2 1 = = =0
x2 − x1 −5 − 4 −9




14. P = ( 2,1) ; m = 4
y2 − y1 −2−2
11. Slope = =
x2 − x1 −1 − (−1)
−4
= undefined.
0




3
15. P = ( 2, 4 ) ; m = −
4




587

,CD Topics to Discuss


2 20. P = ( −2, 0 ) ; slope undefined
16. P = (1,3) ; m = −
5




17. P = ( −1,3) ; m = 0
4
21. Slope = 4 =
1
If x increases by 1 unit, then y
increases by 4 units.
Answers will vary. Three possible
points are:
x = 1 + 1 = 2 and y = 2 + 4 = 6
( 2, 6 )
x = 2 + 1 = 3 and y = 6 + 4 = 10
( 3,10 )
18. P = ( 2, −4 ) ; m = 0 x = 3 + 1 = 4 and y = 10 + 4 = 14
( 4,14 )
2
22. Slope = 2 =
1
If x increases by 1 unit, then y
increases by 2 units.
Answers will vary. Three possible
points are:
x = −2 + 1 = −1 and y = 3 + 2 = 5
( −1,5)
19. P = ( 0,3) ; slope undefined
x = −1 + 1 = 0 and y = 5 + 2 = 7
( 0, 7 )
x = 0 + 1 = 1 and y = 7 + 2 = 9
(1,9 )




588

, CD-1 Lines


3 −3 −1
23. Slope = − = 26. Slope = −1 =
2 2 1
If x increases by 2 units, then y If x increases by 1 unit, then y
decreases by 3 units. decreases by 1 unit.
Answers will vary. Three possible Answers will vary. Three possible
points are: points are:
x = 2 + 2 = 4 and y = −4 − 3 = −7 x = 4 + 1 = 5 and y = 1 − 1 = 0
( 4, −7 ) ( 5, 0 )
x = 4 + 2 = 6 and y = −7 − 3 = −10 x = 5 + 1 = 6 and y = 0 − 1 = −1
( 6, −10 ) ( 6, −1)
x = 6 + 2 = 8 and y = −10 − 3 = −13 x = 6 + 1 = 7 and y = −1 − 1 = −2
(8, −13) ( 7, −2 )
4 27. (0, 0) and (2, 1) are points on the line.
24. Slope =
3 1− 0 1
Slope = =
If x increases by 3 units, then y 2−0 2
increases by 4 units. y -intercept is 0; using y = mx + b :
Answers will vary. Three possible 1
points are: y = x+0
2
x = −3 + 3 = 0 and y = 2 + 4 = 6
2y = x
( 0, 6 ) 0 = x − 2y
x = 0 + 3 = 3 and y = 6 + 4 = 10 1
( 3,10 ) x − 2 y = 0 or y = x
2
x = 3 + 3 = 6 and y = 10 + 4 = 14
28. (0, 0) and (–2, 1) are points on the line.
( 6,14 ) 1− 0 1 1
Slope = = =−
−2 −2−0 −2 2
25. Slope = −2 = y -intercept is 0; using y = mx + b :
1
If x increases by 1 unit, then y 1
y = − x+0
decreases by 2 units. 2
Answers will vary. Three possible 2 y = −x
points are: x + 2y = 0
x = −2 + 1 = −1 and y = −3 − 2 = −5
1
( −1, −5) x + 2 y = 0 or y = − x
2
x = −1 + 1 = 0 and y = −5 − 2 = −7
( 0, −7 )
x = 0 + 1 = 1 and y = −7 − 2 = −9
(1, −9 )




589