Copright Pearson Education, Inc., or its affiliates. All Rights Reserved. Investigation Additional Practice. a. Francine:. mph; Geraldo: mph; Jennifer: 7. mph; Divide the number of miles traveled in hours b. b. Francine: 7 miles; Geraldo: miles; Jennifer: miles. a. Francine: D.t;Geraldo:D t; Jennifer: D 7.t b. Substitute. for t in each question. c. the number being multiplied b t d. Proportional. a. (Figure ) b. Students estimates should be close to the following values: Francine:. miles; Geraldo: miles; Jennifer:.7 miles c. Students estimates should be close to the following values: Francine:. hours; Geraldo:.7 hours; Jennifer: 9. hours d. The faster the cclist, the steeper the graph.. a. 7. miles per hour b. Stilton s graph would be steeper than Francine s and Geraldo s but less steep than Jennifer s. Figure Distance (miles). a. Ccling Trip 00 0 0 0 0 0 0 7 9 0 Time (hours) Jennifer Geraldo Francine 0 b. Sets i, ii, and iii represent linear relationships. The graphs of these data sets are straight lines. c. No; none of the sets contain - and -values that are related b a constant of proportionalit.. a. b. c. does 7. a. B 7w b. The graph is a line. The graph passes through the origin. The graph is increasing.. Number of apples Cost $.0 $ $ 9 $.7 0 i ii iii iv
Skill: Linear Relationships. + a. $77 b. $ 0 ii. - - - iii.... a. $ b. $.0 - - - O - - - iv.. a. 7 in. b. 0 in. - - - O - Investigation Additional Practice. a. i. - b. i. increase ii. decrease iii. decrease iv. increase c. i. (0, 0) ii. (0, 7) iii. (0, ) iv. (0, ) d. i. iv. Answers will var.. a. $; $0 b. $ c. $00 $0 $0. a. (, 7), (9, ), (.9,.) b. (0, ), (, ) c. (,.7), (.7,.). a. Possible answer: (, 0), (0, ), and (, ) b. ii. 0. c. no; The -value corresponds to the -value 0, not. d. es; The -value 0 does correspond to the -value. Copright Pearson Education, Inc., or its affiliates. All Rights Reserved.
Copright Pearson Education, Inc., or its affiliates. All Rights Reserved.. The equation for the line labeled A: ;the equation for the line labeled B: ;the equation for the line labeled C: + a. (Figure ) b. line A:,line B:, line C:. The equation of the line labeled A: ; The equation of the line labeled B: a. The are parallel; the cross the -ais at different points. b. Change the constant value of to c. d. ; is halfwa between and e. No 7. The graph is of the equation. a. b. For each increase in,the value of Figure Line 0 7 0 00 0 9 increases b. So from 0 to 00, which is a change of 90, there is a change of times 90 or. Constant Rate of Change -intercept. a. and (0, 0) and (0, ) and (0, ) and (0, ) b. The -coordinate of the point of intersection is the common constant term in the two equations. c. (0, 7) 9. 0 0 0. 0 0. Yes, the point is (, ), which is where the two lines intersect on the graph. The point (, ) is on both lines so it satisfies both equations.. es. no. es. no. a. b. 9 c. 7.. 9. a. 7 b. 0.,. increasing:,,, decreasing:, -intercept Copright Pearson Education, Inc., or its affiliates. All Rights Reserved. A (0, ) (, 0) B (0, ) (, 0) C (0, ) (, 0) 7
Skill: Linear Functions, Graphs, and Tables. a. = 0. + 0.0 b. miles c. $.7.. a. Equation ii because the point satisfies the equation: 7.(0). b. Answers will var.. a. i.. O - - - WINDOW XM IN = 0 XMAX=0 XSCL= YM IN = 0 YMAX=0 YSCL= O - - - ii.. O - - -. A. A, B 7. B, C. C 9. A 0. B. C. B.. 7.. Investigation Additional Practice. a. Equation iii because the point satisfies the equation: 0 0.(0). b. Answers will var. WINDOW XM IN = 0 XMAX=0 XSCL= YM IN = 0 YMAX= YSCL= Copright Pearson Education, Inc., or its affiliates. All Rights Reserved.
Copright Pearson Education, Inc., or its affiliates. All Rights Reserved. iii. iv. WINDOW XM IN = -0 XMAX=0 XSCL= YM IN = -0 YMAX= YSCL= WINDOW XMIN= 0 XMAX=0 XSCL= YMIN= 0 YMAX=0 YSCL= b. The eact answers are given here. If students found the intersection points b inspecting the graphs, their answers ma not be eact. i. (.,.) ii. (, ) iii. ( 0.,.) iv. (, ) The values ma not fit eactl because the ma be estimates, but the should be close.. a. r b. 0 c. z d. w 7. a. b. ( ) ; this equation is the same as. Subtracting from both sides gives 0, so 0 and.. a. ; b. 7 7; c. ; 7. a. $. b. $ c. $.7 profit d. 9 people e. $9.7 f. 9 tickets g. 7 tickets. a. ; graph is a line with a slope of and -intercept (, 0) b. ; graph is a line with a slope of and -intercept (, 0) c. 0 ;graph is a line with a slope of and -intercept ( 0, 0) d. The solution is the -coordinate of the -intercept. 9. a. Both strategies are correct. b. Answers will var. c. Dividing is reasonable if all the values are divisible b the same number. d. 0. a. b. so c. so d. The numerators of the solutions are all ; the denominators are the coefficients of.. a. b. c. 0 d. e. 0 f.. a..p #,0 b. p 00 #,0 c. First caterer: 9 people or fewer 90 9 00 Second caterer: 9 people or fewer 9
d. Possible Answer: I would choose the second caterer. The first caterer will cost less if there are people or fewer, but Kelli can invite more people with the second caterer.. C 0.g, C 0.g. (, ). :, 0 90 9 00 :,, Skill: Eploring Equalit. a. es b. no c. no d. es. a. no b. es c. es d. es... 9. 7 7. ; ; ;. ; 7; 0; 9. ; ; ; 0. ; ; 9; Skill: Finding the Point of Intersection. Yes; the lines have different slopes, so there will be eactl one -value that corresponds to the same -value for each line.. (, );. a. 0.;.. b.. pounds 0 O 0 0 0 Skill: Solving Linear Equations. h. s 9.. g. j. w 7. $ $m; $. w 0; weeks 9. 0.... 7.. 00 0w 0; weeks. 0 v ; 7 visits Investigation Additional Practice. a. slope is ; -intercept is (0, 0) b. slope is ; -intercept is (0, ) c. slope is ; -intercept is (0,.) d. slope is.; -intercept is (0, 0) e. slope is 7; -intercept is (0, ). i. a.. ii. a. b. (0, 0) b. (0, ) c.. c. iii. a. iv. a. b. (0,.) b. (0, ) c.. c. v. a. b. (0, ) c.. a. slope is ; b. slope is ; c. slope is ;. a. line ii b. i. slope ii. slope c. i. -intercept (0, 0) ii. -intercept (0, 0) line i Copright Pearson Education, Inc., or its affiliates. All Rights Reserved.
Copright Pearson Education, Inc., or its affiliates. All Rights Reserved. d. i. ii.. a. M 0.n.0 b. 0. is slope; It is the cost of each game. c..0 is the -intercept; It is the bus fare. d. $.0 e. Jim can pla 9 games, and he will have $0. left over.. a. $.; This is the intercept on the -ais, which represents the cost if Angie bus 0 comics. b. $.0; For each comic book purchased, the cost rises b $.0. c. Using the slope and the -intercept, the equation is M.n.. This is not a proportional relationship. 7. a. gallons; This is the -intercept (the amount of water in the aquarium at t 0). b. From the graph, the siphon removes 0 gallons in minutes, or equivalentl, 0 c. G t gallons in minute. d. Substitute 0 for t in the equation. You get G. gallons of water left in the aquarium. e. Substitute 0 for G in the equation. You get t 7 minutes.. a. 7 b. 9. c. 0. d. 0 e. 9. The equations for the lines are: Figure Line A: Line B: Line C: Line D: 0 Shape Pattern Pattern Pattern Pattern 0 9 0. a. C.n. b..; This is the cost for shoe rental. c..; This is the cost of bowling each game. d. $.7 e. Ton bowled games.. a. Positive slope, -intercept equals 0, passes through the origin (0, 0) b. Positive slope, positive -intercept, crosses the -ais to the left of the origin c. Slope equals 0, negative -intercept, never crosses the -ais d. Negative slope, positive -intercept, crosses the -ais to the right of the origin e. Negative slope, negative -intercept, crosses the -ais to the left of the origin. (, ); since the equation of the line is:. a. (Figure ) b. The perimeter increases b. c. For Figure, ou can see the pattern is increasing b. For Figure 0, ou know it would be columns to the right of Figure in the epanded table, so the perimeter of each Figure 0 perimeter would be units greater than each Figure perimeter. The perimeter of Figure 00, using the same reasoning, would be 90 0 units greater than the perimeter of Figure 0. d. square: P N, where N number of copies square: P N, where N number of copies square: P N, where N number of copies square: P N, where N number of copies Figure Figure Figure Figure Figure 0 Figure 00 0 0 0 0 0 0 0
. a. The slopes are the same; the -intercepts are different. Another difference is that Line A represents a relationship that is not proportional and Line B represents a relationship that is proportional. b. K, where K is an number strictl between and 0; for eample, ().This line has the same slope but a different -intercept than the first two lines. c. The new line has the same slope, so it is parallel to the original two lines; the new constant term is between the original constant terms, so the -intercept of the new line is between the -intercept of the original two lines.. As increases b, increases b. As decreases b, decreases b.. ; 7.. Positive slope:, Passes through the origin:, Positive -intercept:,, Skill: Finding Slope... 0... 7. O. 9. undefined 0. 0. Skill: Using Slope. es. no. no. no.. 7.. 9. 0. O O Skill: Writing Equations.... $,000. $7. 7. $0. = + 00 Copright Pearson Education, Inc., or its affiliates. All Rights Reserved.