NAME DATE PERIOD. 11. Is the relation (year, percent of women) a function? Explain. Yes; each year is


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1  NAME DATE PERID Functions Determine whether each relation is a function. Eplain.. {(, ), (0, 9), (, 0), (7, 0)} Yes; each value is paired with onl one value.. {(, ), (, ), (, ), (, ), (, )}. No; in the domain is paired with and in the range. 0 No; in the domain is paired with and 0 in the range.. {(, ), (, ), (, ), (, ), (, )} Yes; each value is paired with onl one value.. {(, ), (, ), ( 7, ), (, ), (, ), ( 7, )}. No; 7 in the domain is paired with and in the range Yes; each value is paired with onl one value. Lesson No;.0 in the domain is paired with. and.7 in the range. No; in the domain is paired with and in the range. EMPLYMENT For Eercises 9, use the table, which shows the percent of emploed men and women in the U.S. labor force ever five ears from 90 to Is the relation (ear, percent of men) a function? Eplain. Yes; each ear is paired with onl one value for the percent of emploed men. 0. Describe how the percent of emploed men is related to the ear. The number of emploed men varies each ear, but is around 7 percent of the male population. Year Emploed Members of Labor Force Men Women (% of male (% of female population) population) Source: U.S. Census Bureau. Is the relation (ear, percent of women) a function? Eplain. Yes; each ear is paired with onl one value for the percent of emploed women.. Describe how the percent of emploed women is related to the ear. As the ears progress, the percent of emploed women increases. Glencoe/McGrawHill 9 Glencoe PreAlgebra
2  NAME DATE PERID Linear Equations in Two Variables Find four solutions of each equation. Write the solutions as ordered pairs.. Sample answers are given (, ), (0, ), (, 7), (0, 7), (, ), (0, ), (, ), (, ) (, 7), (, 7) (, ), (, )... 7 (, 7), (0, ), (, ), (0, ), (, ), (0, ), (, ), (, ) (, ), (, ) (, 7), (, 0) Graph each equation b plotting ordered pairs CKING For Eercises, use the following information. Kirsten is making gingerbread cookies using her grandmother s recipe and needs to convert grams to ounces. The equation 0.0 describes the approimate number of ounces in grams.. Find three ordered pairs of values that satisf this equation. Sample answer: (00, ), (00, ), (00, ). Draw the graph that contains these points.. Do negative values of make sense in this case? Eplain. No; a recipe cannot contain a negative number of grams of an ingredient. Glencoe/McGrawHill Glencoe PreAlgebra unces Grams
3  NAME DATE PERID Graphing Linear Equations Using Intercepts Find the intercept and the intercept for the graph of each equation , none,, ,, 7, none Graph each equation using the  and intercepts (7, 0) (0, 7) (0, ) + (, 0) (0, ) (, 0) (7, 0) (0, ) 7 + (0, ) (, 0) (, 0) Lesson . SAVINGS Rashid s grandparents started a savings account for him, contributing $000. He deposits $0 each month into the account. The equation represents how much mone is in the savings account after number of months. Graph the equation and eplain what the intercept means. The intercept 000 shows how much mone was in the savings account before Rashid made an deposits. $ (thousand) Months Glencoe/McGrawHill 9 Glencoe PreAlgebra
4  NAME DATE PERID Slope Find the slope of each line.... (, ) (0, ) (0, ) (, ) (0, ) (, ) Find the slope of the line that passes through each pair of points.. A( 0, ), B(, ). C(7, ), D(, ). E(, ), F(, ) 7 7. G(, 7), H( 0, ). J(, 0), K(, ) 9. L(, ), M(, 9) 0. P(, ), Q(, ). R(, ), S(, ). T(, ), U(, ) undefined 0. CAKES A wedding cake measures feet high in the center and the diameter of the bottom tier is inches. What is the slope of the cake?. INSECTS ne particularl large ant hill found in 997 measured 0 inches wide at the base and inches high. What was the slope of the ant hill? 9 0. ARCHAELGY Toda, the Great Pramid at Giza near Cairo, Egpt, stands 7 meters tall, coming to a point. Its base is a square with each side measuring 0 meters wide. What is the slope of the pramid? 7. BUSINESS ne warehouse uses foot long ramps to load its forklifts onto the flat beds of trucks for hauling. If the bed of a truck is feet above the ground and the ramp is secured to the truck at its end, what is the slope of the ramp while in operation? Glencoe/McGrawHill Glencoe PreAlgebra
5  NAME DATE PERID Rate of Change Find the rate of change for each linear function.. 0. Air in Tires (psi) Time Distance (h) (km) Time (min) decrease of psi/min increase of 0 km/h Suppose varies directl with. Write an equation relating and.. when. 7 when 9. when. 0 when 7. when 7. when 9.. when 9 0. when. when 0.. when 7. when. when 9 TRAFFIC MANAGEMENT For Eercises and, use the following information. San Diego reserves epress lanes on the freewas for the use of carpoolers. In order to increase traffic flow during rush hours, other drivers ma use the epress lanes for a fee. The toll varies directl with the number of cars on the road. The table shows a sample of possible tolls.. Write an equation that relates the toll and traffic volume.. Predict the number of vehicles at a peak time if the toll increases to $.00. vehicles/h Toll Traffic Volume ($) (vehicles/h) FFICE SUPPLIES The cost of paper varies directl with the number of reams of paper purchased. If reams cost $9.0, find the cost of reams. $9.0 Lesson  Glencoe/McGrawHill 9 Glencoe PreAlgebra
6  NAME DATE PERID SlopeIntercept Form Given the slope and intercept, graph each line.. slope,. slope,. slope, intercept intercept intercept + Graph each equation using the slope and intercept.... EXERCISE For Eercises 7 and, use the following information. A person weighing 0 pounds burns about 0 Calories per hour walking at a moderate pace. Suppose that the same person burns an average of 00 Calories per da through basic activities. The total Calories burned b that person can be represented b the equation 0 00, where represents the number of hours spent walking. 7. Graph the equation using the slope and intercept. Calories Burned (thousands) State the slope and intercept of the graph of the equation and describe what the represent. The intercept 00 represents the number of Calories burned without eercising. The slope 0 represents the number of Calories burned per hour when walking Time Walking (h) Glencoe/McGrawHill Glencoe PreAlgebra
7 7 NAME DATE PERID Writing Linear Functions Write an equation in slopeintercept form for each line.. slope,. slope 0, intercept intercept Lesson 7 Write an equation in slopeintercept form for the line passing through each pair of points.. (9, 0) and (, ). (, ) and (, ) 7. (7, ) and (, ). (, 7) and (, ) 9. (, ) and (, 0) 0. (0, ) and (, ) BUSINESS For Eercises and, use the following information. Flourishing Flowers charges $ plus $0 for each standard floral arrangement to deliver and set up flowers for a banquet.. Write an equation in slopeintercept form that shows the cost for flowers for number of arrangements. 0. Find the cost of providing 0 floral arrangements. $ INSULATIN For Eercises and, use the following information. Renata González wants to increase the energ efficienc of her house b adding to the insulation previousl installed. The better a material protects against heat loss, the higher its Rvalue, or resistance to heat flow. The table shows the Rvalue of fiberglass blanket insulation per inch of thickness. The eisting insulation in Renata s attic has an Rvalue of 0.. Write an equation in slopeintercept form that shows the total Rvalue in the attic if she adds number of inches of additional insulation.. 0 Rvalue. Estimate the total Rvalue in the attic if she adds inches of insulation. 9. Thickness (in.) Source: ak Ridge National Laborator Glencoe/McGrawHill 9 Glencoe PreAlgebra
8 Glencoe/McGrawHill A Glencoe PreAlgebra  NAME DATE PERID Functions Determine whether each relation is a function. Eplain.. {(, ), (0, 9), (, 0), (7, 0)} Yes; each value is paired with onl one value.. {(, ), (, ), (, ), (, ), (, )}. 7. No; in the domain is paired with and in the range. 0 No; in the domain is paired with and 0 in the range No;.0 in the domain is paired with. and.7 in the range.. {(, ), (, ), (, ), (, ), (, )} Yes; each value is paired with onl one value.. {(, ), (, ), ( 7, ), (, ), (, ), ( 7, )} No; 7 in the domain is paired with and in the range. Glencoe/McGrawHill 9 Glencoe PreAlgebra Yes; each value is paired with onl one value. 7 7 No; in the domain is paired with and in the range. EMPLYMENT For Eercises 9, use the table, which shows the percent of emploed Emploed Members of Labor Force men and women in the U.S. labor force Men Women ever five ears from 90 to 000. Year (% of male (% of female 9. Is the relation (ear, percent of men) a population) population) function? Eplain. Yes; each ear is paired with onl one value for the percent of emploed men Describe how the percent of emploed men is related to the ear. The number of emploed men varies each ear, but is around 7 percent of the male population. Source: U.S. Census Bureau. Is the relation (ear, percent of women) a function? Eplain. Yes; each ear is paired with onl one value for the percent of emploed women.. Describe how the percent of emploed women is related to the ear. As the ears progress, the percent of emploed women increases. Lesson   PreActivit NAME DATE PERID Reading to Learn Mathematics Functions Reading the Lesson How can the relationship between actual temperatures and windchill temperatures be a function? Do the activit at the top of page 9 in our tetbook. Write our answers below. a. n grid paper, graph the temperatures as ordered pairs (actual, windchill). b. Describe the relationship between the two temperature scales. Sample answer: As the actual temperature increases, the windchill temperature also increases. c. When the actual temperature is 0 F, which is the best estimate for the windchill: F, F, or 0 F? Eplain. F; when the actual temperature decreases, the windchill temperature also decreases.. See students work. Write a definition and give an eample of each new vocabular word or phrase. Vocabular Definition Eample. function. vertical line test For a relation to be a function, each element in the domain must have onl one corresponding element in the range.. Eplain what is meant b the phrase distance is a function of time. Sample answer: How far something travels depends on how much time elapses. Helping You Remember. You have learned various was to determine whether a relation is a function. Choose which method is the easiest for ou to use, then write a few sentences eplaining how that method relates to the other methods. Sample answer: Placing the range values in a table with their corresponding domain values makes it eas to see whether an element in the domain is paired with onl one element in the range. B graphing and connecting the points, the vertical line test can be applied to arrive at the same answer. Glencoe/McGrawHill 0 Glencoe PreAlgebra Answers (Lesson ) Answers
9 Glencoe/McGrawHill A Glencoe PreAlgebra  NAME DATE PERID Skills Linear Equations in Two Variables Find four solutions of each equation. Write the solutions as ordered pairs. 9. Sample answers are given.. =.. (, ), (0, ), (, ), (0, ), (, 7), (0, ), (, ), (, ) (, ), (, 0) (, ), (, ).. 7. (, ), (0, ), (, ), (0, ), (, ), (0, ), (, ), (, 7) (, ), (, ) (, ), (, ) (, ), (0, ), (, ), (0, 0), (, ), (0, ), (, ), (, ) (, ), (, ) (, 0), (, ) Graph each equation b plotting ordered pairs } } } }... } } Glencoe/McGrawHill Glencoe PreAlgebra + Lesson   NAME DATE PERID Linear Equations in Two Variables Find four solutions of each equation. Write the solutions as ordered pairs.. Sample answers are given (, ), (0, ), (, 7), (0, 7), (, ), (0, ), (, ), (, ) (, 7), (, 7) (, ), (, )... 7 (, 7), (0, ), (, ), (0, ), (, ), (0, ), (, ), (, ) (, ), (, ) (, 7), (, 0) Graph each equation b plotting ordered pairs } } CKING For Eercises, use the following information. Kirsten is making gingerbread cookies using her grandmother s recipe and needs to convert grams to ounces. The equation 0.0 describes the approimate number of ounces in grams.. Find three ordered pairs of values that satisf this equation. Sample answer: (00, ), (00, ), (00, ). Draw the graph that contains these points.. Do negative values of make sense in this case? Eplain. No; a recipe cannot contain a negative number of grams of an ingredient. 0 + Glencoe/McGrawHill Glencoe PreAlgebra unces Grams Answers (Lesson ) Answers
10 Glencoe/McGrawHill A Glencoe PreAlgebra  NAME DATE PERID Graphing Linear Equations Using Intercepts Find the intercept and the intercept for the graph of each equation , none,, ,, 7, none Graph each equation using the  and intercepts (7, 0) (0, 7) 0. } } (7, 0) (0, ) 7 (0, ) + (, 0) + (0, ) (, 0). SAVINGS Rashid s grandparents started a savings account for him, contributing $000. He deposits $0 each month into the account. The equation represents how much mone is in the savings account after number of months. Graph the equation and eplain what the intercept means. The intercept 000 shows how much mone was in the savings account before Rashid made an deposits. (, 0) Glencoe/McGrawHill 9 Glencoe PreAlgebra $ (thousand) 0 (0, ) (, 0) 0 0 Months Lesson   PreActivit NAME DATE PERID Reading to Learn Mathematics Graphing Linear Equations Using Intercepts Reading the Lesson How can intercepts be used to represent reallife information? Do the activit at the top of page in our tetbook. Write our answers below. a. Write the ordered pair for the point where the graph intersects the ais. What does this point represent? (0, ); a temperature of 0 C equals F. b. Write the ordered pair for the point where the graph intersects the ais. What does this point represent? (, 0); a temperature of approimatel C equals 0 F.. See students work. Write a definition and give an eample of each new vocabular word. Vocabular Definition Eample. intercept. intercept. The coordinate of the intercept is 0. The coordinate of the intercept is 0.. Draw a model on the coordinate grid that shows how to graph a line using the intercept and the intercept of a line. Eplain our model. (0, ) (, 0) Sample answer: The intercept is, which means that one point of the graph is at (, 0). The intercept is, which means that another point of the graph is at (0, ). Graph both points on the grid and draw a line through them.. Is a line with no intercept vertical or horizontal? Eplain. Horizontal; if a line has no intercept, the line will never cross the ais. Therefore, the line must be parallel to the ais. Helping You Remember. The word intercept has man snonms in English. Look up intercept in a thesaurus and find one or two snonms that help ou remember the mathematical meaning of the word. Eplain our selection. Sample answer: cut off; The intercept is where the ais cuts off the line; the intercept is where the ais cuts off the line. Glencoe/McGrawHill 0 Glencoe PreAlgebra Answers (Lesson )
11 Glencoe/McGrawHill A0 Glencoe PreAlgebra  NAME DATE PERID Skills Slope Find the slope of each line.... (, ) } }... (0, ) (0, ) (0, ) (, ) (0, ) } } Find the slope of the line that passes through each pair of points. 7. A(, ), B(, 7). C(7, ), D(, ) 9. E(7, ), F(, ) } } } } 0. G(, ), H(, ). J(, 9), K(0, ). L(, ), M(, ) } } } } } }. P(, ), Q(7, ). R(, ), S(, ). T(, ), U(, ) } } undefined. P(0, ), Q(, ) 7. R(, ), S(7, ). T(, ), U(7, ) } 7 } 0 9. CAMPING A famil camping in a national forest builds a temporar shelter with a tarp and a foot pole. The bottom of the pole is even with the ground, and one corner is staked feet from the bottom of the pole. What is the slope of the tarp from that corner to the top of the pole? } } 0. ART A rectangular painting on a galler wall measures 7 meters high and meters wide. What is the slope from the upper left corner to the lower right corner? } 7 } Glencoe/McGrawHill Glencoe PreAlgebra (, ) (, ) (, ) (0, ) (, ) (0, ) Lesson   NAME DATE PERID Slope Find the slope of each line.... } } Find the slope of the line that passes through each pair of points.. A( 0, ), B(, ). C(7, ), D(, ). E(, ), F(, ) } } } } } 7 } 7. G(, 7), H( 0, ). J(, 0), K(, ) 9. L(, ), M(, 9) } } } } 0. P(, ), Q(, ). R(, ), S(, ). T(, ), U(, ) } } undefined 0. CAKES A wedding cake measures feet high in the center and the diameter of the bottom tier is inches. What is the slope of the cake?. INSECTS ne particularl large ant hill found in 997 measured 0 inches wide at the base and inches high. What was the slope of the ant hill? 9 } } 0. ARCHAELGY Toda, the Great Pramid at Giza near Cairo, Egpt, stands 7 meters tall, coming to a point. Its base is a square with each side measuring 0 meters wide. What is the slope of the pramid? } } 7. BUSINESS ne warehouse uses foot long ramps to load its forklifts onto the flat beds of trucks for hauling. If the bed of a truck is feet above the ground and the ramp is secured to the truck at its end, what is the slope of the ramp while in operation? } } (, ) (0, ) Glencoe/McGrawHill Glencoe PreAlgebra (0, ) (, ) (0, ) (, ) Answers (Lesson )
12 Glencoe/McGrawHill A Glencoe PreAlgebra  NAME DATE PERID Rate of Change Find the rate of change for each linear function.. 0. Time Distance 0 (h) (km) Air in Tires (psi) Time (min) decrease of psi/min increase of 0 km/h Suppose varies directl with. Write an equation relating and.. when. 7 when 9. when } }. 0 when 7. when 7. when } } 9.. when 9 0. when. when 0. } }. when 7. when. when 9 TRAFFIC MANAGEMENT For Eercises and, use the following information. San Diego reserves epress lanes on the freewas for the use of carpoolers. In order to increase traffic flow during rush hours, other drivers ma use the epress lanes for a fee. The toll varies directl with the number of cars on the road. The table shows a sample of possible tolls.. Write an equation that relates the toll and traffic volume.. Predict the number of vehicles at a peak time if the toll increases to $.00. vehicles/h Toll Traffic Volume ($) (vehicles/h) FFICE SUPPLIES The cost of paper varies directl with the number of reams of paper purchased. If reams cost $9.0, find the cost of reams. $9.0 Glencoe/McGrawHill 9 Glencoe PreAlgebra Lesson   PreActivit NAME DATE PERID Reading to Learn Mathematics Rate of Change Reading the Lesson How are slope and speed related? Do the activit at the top of page 9 in our tetbook. Write our answers below. a. For ever hour increase in time, what is the change in distance? mi b. Find the slope of the line. c. Make a conjecture about the relationship between slope of the line and speed of the car. Slope is equal to the speed of the car.. See students work. Write a definition and give an eample of each new vocabular phrase. Vocabular Definition Eample. rate of change. direct variation. constant of variation Complete each sentence.. Rates of change can be described using slope.. Direct variation is a special tpe of linear equation. Helping You Remember. The word ratio comes from the Latin word meaning rate and can also mean proportion or relation. Direct variation is often called direct proportion. Look up ratio in the dictionar. Then use this information to eplain the relationship between rate of change and direct variation. Sample answers: The rate of change is the ratio of the change in one quantit to the change in another quantit. If the ratio is direct, or proportional, then both quantities var at the same, or constant, rate. Either the both increase at the same rate or the both decrease at the same rate. Glencoe/McGrawHill 0 Glencoe PreAlgebra Answers (Lesson ) Answers
13 Glencoe/McGrawHill A Glencoe PreAlgebra  NAME DATE PERID Skills SlopeIntercept Form State the slope and the intercept for the graph of each equation... } }. ; } } ; ; Given the slope and intercept, graph each line.. slope,. slope } },. slope } }, intercept intercept intercept Graph each equation using the slope and intercept. 7.. } } Glencoe/McGrawHill Glencoe PreAlgebra + + Lesson   NAME DATE PERID SlopeIntercept Form Given the slope and intercept, graph each line.. slope } },. slope } },. slope, intercept intercept intercept Graph each equation using the slope and intercept.. } }.. Calories Burned (thousands) Time Walking (h) + Glencoe/McGrawHill Glencoe PreAlgebra EXERCISE For Eercises 7 and, use the following information. A person weighing 0 pounds burns about 0 Calories per hour walking at a moderate pace. Suppose that the same person burns an average of 00 Calories per da through basic activities. The total Calories burned b that person can be represented b the equation 0 00, where represents the number of hours spent walking. 7. Graph the equation using the. State the slope and intercept of the slope and intercept. graph of the equation and describe what the represent. The intercept 00 represents the number of Calories burned without eercising. The slope 0 represents the number of Calories burned per hour when walking. Answers (Lesson ) Answers
14 Glencoe/McGrawHill A Glencoe PreAlgebra 7 NAME DATE PERID Writing Linear Functions Write an equation in slopeintercept form for each line.. slope,. slope 0, intercept intercept } } Write an equation in slopeintercept form for the line passing through each pair of points.. (9, 0) and (, ). (, ) and (, ) 7. (7, ) and (, ) } } } }. (, 7) and (, ) 9. (, ) and (, 0) 0. (0, ) and (, ) } } BUSINESS For Eercises and, use the following information. Flourishing Flowers charges $ plus $0 for each standard floral arrangement to deliver and set up flowers for a banquet.. Write an equation in slopeintercept form that shows the cost for flowers for number of arrangements. 0. Find the cost of providing 0 floral arrangements. $ INSULATIN For Eercises and, use the following information. Renata González wants to increase the energ efficienc of her Thickness house b adding to the insulation previousl installed. The better Rvalue (in.) a material protects against heat loss, the higher its Rvalue, or resistance to heat flow. The table shows the Rvalue of fiberglass blanket insulation per inch of thickness. The eisting insulation in Renata s attic has an Rvalue of 0.. Write an equation in slopeintercept form that shows the total Rvalue in the attic if she adds number of inches of additional insulation Estimate the total Rvalue in the attic if she adds inches of insulation. 9. Glencoe/McGrawHill 9 Glencoe PreAlgebra Source: ak Ridge National Laborator Lesson 77 PreActivit NAME DATE PERID Reading to Learn Mathematics Writing Linear Functions Reading the Lesson How can ou model data with a linear equation? Do the activit at the top of page 0 in our tetbook. Write our answers below. a. Graph the ordered pairs (chirps, temperature). Draw a line through the points. Temperature ( F) Number of Chirps b. Find the slope and the intercept of the line. What do these values represent? Slope represents the rate of change, degree for ever chirp; intercept 0 represents the temperature at which the crickets are not chirping. c. Write an equation in the form m b for the line then translate the equation into a sentence. 0; The temperature equals the number of chirps in seconds plus 0.. Eplain how ou can use the following information to write the slopeintercept form of a line. a. graph of a line Find the intercept. From that point, count how man units up or down and how man units left or right to another point. The slope is the ratio of the rise over the run. Then substitute the slope and the intercept into the slopeintercept form. b. two points on a line Substitute the coordinates of two points on the line into the definition of slope. Then use the slope and one of the points to find the intercept. Substitute the slope and the point s coordinates into slopeintercept form. Then substitute the slope and the intercept into the slopeintercept form. c. a table of values Use the table to identif the coordinates of two points on the line. Then substitute the coordinates of the two points on the line into the definition of slope. Then use the slope and one of the points to find the intercept. Substitute the slope and the point s coordinates into slopeintercept form. Then substitute the slope and the intercept into the slopeintercept form. Glencoe/McGrawHill 0 Glencoe PreAlgebra Answers (Lesson 7)
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