2. Bunny Slope:, Medium Trail: 4. 58; The starting height of the trail is 58 meters ; The length of the trail is 1450 meters.

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1 ...7 Start Thinking! For use before Lesson.7 Sample answer: If ou need to write the equation of a line given the slope and a point on the line, ou can find the -intercept (either graphicall or algebraicall). Then ou follow the steps for writing an equation given the slope and -intercept..7 Warm Up For use before Lesson.7. = x. = x +. = x..7 Practice A. = x +. = x = x +. + = ( x ). = ( x + ). = ( x ). + = ( x + ) 7. = x 8. = x + 9. = x 0. = x +. a. V = 0x b. $900 c. $0.7 Practice B. = x. = x +. = ( x + ). + 7 = ( x 8). + = ( x + ). 8 = ( x + ) 7. = x O x = x = x + 0. = x x. a. = x + b. feet c. after seconds.7 Enrichment and Extension. The slope is the negative of the grade, written as a fraction or decimal.. Bunn Slope:, Medium Trail: Expert Trail: 0. = x + 8, 0. 8; The starting height of the trail is 8 meters.. 0; The length of the trail is 0 meters.. = x no; It has a grade of 8%..7 Puzzle Time THE TEAM SPIRIT Technolog Connection... a.. = x b. The sign changed. c. Sample answer: Visualize the points and determine whether the slope should be positive or negative to check our answer.. a. 0.7 b. The are reciprocals. c. Sample answer: Compare the change in to the change in x to determine whether the slope is steeper (magnitude greater than ) or shallower (magnitude less than ) to check our answer Chapter. Start Thinking! For use before Activit. The onl solution is (, ). Methods ma var. Sample answer: Trial and error, to find two numbers where one number is greater than the other and whose sum is. Other methods are substitution and graphing. A

2 . Warm Up For use before Activit... O x x O. (, 7 ). (, ) 7. (, 0) 8. x + = 0 x = 0 one-bedroom apartments, 0 two-bedroom apartments 9. es; The two lines could be parallel..... O O. Start Thinking! For use before Lesson. The solution is (, ). Sample answer: It s easier to see from the graph since ou can see where the two lines intersect. With the table, ou have to look at all of the values to see the ones in which the -values are equal. In general, a graph is easier to use than a table because the solution ma be excluded from the table.. Warm Up For use before Lesson.. (, 0 ). (, 80 ). (, 80 ). (, ). (, 7 ). (, 0 ). Practice A. B. A. C. (, ). (, ). (, ) 7. a. R = x b. bracelets 8. a. x + = x = + b. pens, 9 pencils x x O x O x 0. a. min b. 0 min c. the tortoise. Enrichment and Extension The solutions of the sstems reading across are: 0, 0;, ; 7, ;, ;, ;, ; 8, ;, ;, ; no solution;, ;, ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ). Puzzle Time THE TEACHER TOLD HIM IT WAS A PIECE OF CAKE. Start Thinking! For use before Activit. ( A) A = A = + 0.A 0.A = 0. ( A) = ( ) A = 0 C = = + = 7 ( ) Amelia is 0 and Caleb is 7.. Warm Up For use before Activit.. = x +. b = a. x =. c. = x + 8. x 7 = d + = +. Practice B. (, ). (, ). ( 8, ). a. R = x b. 0 tickets A

3 . Start Thinking! For use before Lesson. Check students solutions. The solutions are (, ) and (, ). The second sstem is easier to solve b graphing because the equations are in a form that is eas to graph. Also solving it b substitution involves fraction operations, which can be trick. The first sstem is easier to solve b substitution. Graphing the second equation in the first sstem can be tough because the -intercept is... Warm Up For use before Lesson. For Exercises, answers will var. Sample answers are given.. x + =. = x + x = x =. x = x = 0. x + = x =. = x x + =. x + = 7 x =. Practice A. = x ; It is alread solved for.. x = ; Ever term is divisible b, so ou can easil solve for x.. 8; x + = Can easil solve for.. (, ). (, 0). ( 7, ) 7. a. x + = = x + 7 b. 9 treadmills c. stationar bikes 8. ( 7, ) 9. (, ) 0.. a. x + = x = b. 8 spoons c. forks. x + = = x + length: cm; width: cm 0,. Practice B. (, ). (, ). a. 08x + = 0 = x + 0 b. $9 c. $9. ( 7, 8 ). (, ) 9. a. x + = 98 x = 9 7.., b. food tents c. retail tents, a. 9 two-ear-olds b. 8 three-ear-olds c. 8 four-ear-olds. Enrichment and Extension. Sample answer: = x, = x. =, x x =. Sample answer: = x, =. = x +, x =. Sample answer: = x +, = x. = x, = x + 7. x =, = x + 8. = x +, = x + 9. = x +, x = 0. = x, = x +. = x +, = x +. Sample answer: = x +, = x +. Sample answer: x + = = x + 7. Puzzle Time IN A POLE VAULT. cars; 8 trucks A7

4 . Start Thinking! For use before Activit. Operation : + 7 = 0 + = + = Operation : + = 0 + = = Yes, after completing the operations, the statements are true. You can use the method of adding the equations together to solve the sstem: A8 x + = 0 x = x = x = 7 x = 7, so 7 + = 0, and =. The solution of the sstem is 7,.. Warm Up For use before Activit. ( ). =. x =. x =. = 9. x =. = 7. Start Thinking! For use before Lesson. Both students used elimination to correctl solve the sstem. Maddie multiplied the second equation b, added the new equation to the first equation, and solved for. Sophie multiplied the second equation b, added the new equation to the first equation, and solved for x. Each student used substitution to correctl solve for the second variable.. Warm Up For use before Lesson.. ( 8.,. ). (, 7). ( 8., ). (, 8). Practice A. (, ). (, ). (, ). a. x + = 9 x + = 7 b. $ per pound c. $ per pound. (, ). (, 0 ) 7. (, ) 8. a. x + = 0 x + 8 = 00 b. multiple choice c. 8 short response d. multiple choice, short response 9. a. es b. You added the equations instead of subtracting them.. Practice B. ( 0, 0 ). (, ). ( 8, ). a. x + = x = 8 b. 7 magazine subscriptions c. magazine subscriptions. (, ). (, ) 7. (, ) 8. a. Sample answer: a = b. Sample answer: b = 9. $90 0. a. a = b. b = c. c =. Enrichment and Extension. Sample answer: It is best to use graphing when both equations are in a form that is eas to graph and the solution has integer values. It is best to use substitution when one or both of the equations are alread solved for one of the variables. It is best to use elimination if it is difficult to solve for one of the variables in one of the equations.. Sample answer: The advantage to graphing is that ou can visualize the solution and how the lines intersect. The disadvantages are that it can take more time to graph, and if the answer is not at a point where the grid squares cross, ou cannot find the solution b graphing. The advantage to substitution is that ou can alwas find the correct answer. The disadvantage is that sometimes solving for one of the variables is trick, especiall if it involves a lot of fractions. The advantage to elimination is that ou can alwas use the method. It is quicker than the other methods if the equations are hard to solve for one of the variables. The disadvantage is that there are often more steps, thus more places to make calculation errors.

5 . Sample answer: I prefer elimination because it works in all situations and I don t have to bother to solve one of the equations for one of the variables.. graphing; (, ). elimination; (, ). substitution; (, 8) 7. graphing; (, ) 8. elimination; (, ) 9. elimination; (, 7) 0. substitution; ( 7, ). substitution; ( 0, ). Puzzle Time SECOND BASE TO THIRD BASE BECAUSE THERE IS A SHORTSTOP. Start Thinking! For use before Activit. Sample answer: No, a pair of numbers cannot add up to two different numbers. The sstem has no solution. Another sstem with no solution is: = x = x +. Warm Up For use before Activit.. parallel. coincide. intersect at one point. coinside. intersect at one point. parallel. Start Thinking! For use before Lesson. Sample answer: In both instances with no solution, ou go through all of the steps of solving and end up with a false statement, such 0 =. The two processes are different because solving a sstem first involves eliminating one of the variables to get an equation in one variable. In solving an equation with a solution of all real numbers or solving a sstem with infinitel man solutions, ou go through all of the steps of solving and end up with a statement that is alwas true, such as =. The two processes are different because solving a sstem first involves eliminating one of the variables to get an equation in one variable.. Warm Up For use before Lesson.. no solution. x = 0., =.. x = 0, = 0. no solution. Practice A. infinitel man solutions; The lines are identical.. no solution; The lines have the same slope and different -intercepts.. one solution; The lines have different slopes.. no solution. (, 7). infinitel man solutions 7. no 8. a. es; If the slopes are different, then the -intercept is the one solution. b. no; The -intercept is a solution to the sstem. c. es; If both equations have the same slope, then the are the same line. 9. There is no such two-digit number. The sstem has no solution. 0. a = 8, b =. Practice B. no solution. (, ). no solution. infinitel man solutions. ( 0, 0 ). infinitel man solutions 7. infinitel man solutions 8. Yes, if the -intercepts are the same. If the -intercepts are different, then the sstem has no solution. 9. a. = x + = x b. no; The sstem has no solution. 0. Sample answer:. Sample answer: x + = x = x + = x + =. Sample answer: = x + = x. a =, bis an number except. A9

6 . Enrichment and Extension. a =, b =. a =, b =. a =, b =. a =, b =. a =, b is an number except.. a =, b = 7. a =, b = 8. a =, b = 9. Check students work.. Puzzle Time PAY HIM Extension. Start Thinking! For use before Extension. Sample answer: The graph shows the linear equations related to each side of the equation. The x-coordinate of the point of intersection is the solution of the equation. Extension. Warm Up For use before Extension.. m = 8. x =. p =. x = 7. r =. x = Extension. Practice. x =. x =. x =. x =. no; You cannot have 8 CDs.. x = 8 7. x =. 8. no; The graph of the sstem = 0 x and = 7 x is a pair of parallel lines. 9. a. x = x 0 b. $0 c. $0 d. Sample answer: the cost of the lemonade Technolog Connection. (, 7 ). (., ). (, 0). (, ) Chapter. Start Thinking! For use before Activit. will var depending on the cost of milk. For example, if one milk costs $0., then the entries in the mapping diagram would be $0., $0.0, $0.7, and $.00. A mapping diagram maps one value to another.. Warm Up For use before Activit.. x =... x = 7.. Start Thinking! For use before Lesson. x =. x = 7. x =. x = The output is. Observe students plaing the Guess the Function Game.. Warm Up For use before Lesson.. Add ; missing entries are 8, 9, and 0.. Multipl b ; missing entries are 0,, and 0.. Practice A. As each input increases b, the output increases b. Input Output 9 8. As each input increases b, the output increases b. Input Output 0 8 A0