Slope is the ratio of the rise, or the vertical change, to the run, or the horizontal change. A greater ratio indicates a steeper slope.

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1 7 NAME DATE PERID Stud Guide Pages Slope Slope is the ratio of the rise, or the vertical change, to the run, or the horizontal change. A greater ratio indicates a steeper slope. A tpical ski mountain has a slope of about 4, while a car windshield ma have a slope of. Eamples: For an two points (, ) and (, ), slope m Find the slope of the line containing each pair of points. a. (4, ) and (, 7) b. (, 6) and (, ) c. (4, ) and (, ) m m m 7 ( ) 4 m m m 9 change in change in 6 ( ) m m m 7 6 or Since ou cannot divide b, the slope is undefined. Determine the slope of the line passing through the points whose coordinates are listed.. (, ) and (4, ). (, ) and (4, ) 7 4. (, ), (, 7) 4. (4, ) and (4, ). (8, ) and (, ) 6. (, ) and (, ) 7. (7, ) and (6, 6) 8. (, ) and (, ) 9. (7, 7) and ( 6, 6). (4, 4) and (, ). (, 4) and (, 9). (, 8) and (, 8) Glencoe/McGraw-Hill 4 Algebra: Concepts and Applications

2 7 NAME DATE PERID Practice Pages Slope Determine the slope of each line.... ( 4, 6) (, 4) (4, ) (, ) ( 4, ) (, ) ( 4, ) (4, ) (, ) (, ) (, ) (, 4) Determine the slope of the line passing through the points whose coordinates are listed in each table Determine the slope of each line the line through points. the line through points at (, 4) and (4, 6) at (, ) and (, ) the line through points. the line through points at (, ) and (, ) at (4, ) and (9, 6) 4. the line through points. the line through points at ( 4, 4) and ( 9, 8) at ( 6, ) and (7, ) Glencoe/McGraw-Hill 4 Algebra: Concepts and Applications

3 7 NAME DATE PERID Enrichment Pages Treasure Hunt with Slopes Using the definition of slope, draw lines with the slopes listed below. A correct solution will trace the route to the treasure. Treasure Start Here no slope Glencoe/McGraw-Hill 4 Algebra: Concepts and Applications

4 7 NAME DATE PERID Stud Guide Pages 9 9 Writing Equations in Point-Slope Form You can write the equation of a line if ou know its slope and the coordinates of one point or if ou know the coordinates of two points on the line. Use the point-slope form. Point-Slope Form For a nonvertical line through the point at (, ) with slope m, the point-slope form of a linear equation is m( ). Eamples: Write the point-slope form of an equation for each line. a. the line passing through the point at ( 4, ) and having a slope of m( ) ( ( 4)) ( 4) b. the line passing through points at (4, 4) and (, ) m Find m. m ( 4) 4 7 or ( 4) ( 4) Substitute m. 4 7 ( 4) Write the point-slope form of an equation for each line, given either the coordinates of a point and the slope or the coordinates of two points.. (, ), m. (4, ), m. (, ), m 7 4. (4, ), m. (8, ), m 6. (, ), m 7. (7, ) and (6, 6) 8. (, ) and (, ) 9. (7, 7) and ( 6, 6). (4, 4) and (, ). (, 4) and (, 9). (, 8) and (, 8) Glencoe/McGraw-Hill 4 Algebra: Concepts and Applications

5 7 NAME DATE PERID Practice Pages 9 9 Writing Equations in Point-Slope Form Write the point-slope form of an equation for each line passing through the given point and having the given slope.. (4, 7), m. (, ), m. (6, ), m 4. (, ), m. ( 4, 6), m 6. ( 8, ), m 7. (7, 9), m 4 8. ( 6, ), m 9. (, ), m 8 Write the point-slope form of an equation for each line... ( 4, 4) ( 4, ) ( 6, 4) (, ).. (6, ) (, ) (, ) (, 4) 4. the line through points. the line through points at (, ) and (, 6) at ( 7, ) and (, ) Glencoe/McGraw-Hill 4 Algebra: Concepts and Applications

6 7 NAME DATE PERID Enrichment Pages 9 9 Celsius and Kelvin Temperatures If ou blow up a balloon and put it in the refrigerator, the balloon will shrink as the temperature of the air in the balloon decreases. The volume of a certain gas is measured at Celsius. The temperature is decreased and the volume is measured again. Temperature (t) C C C C 7 C Volume (v) ml 96 ml 8 ml 74 ml 64 ml. Graph this table on the coordinate plane provided below. v (ml) t( C). Find the equation of the line that passes through the points ou graphed in Eercise.. Use the equation ou found in Eercise to find the temperature that would give a volume of zero. This temperature is the lowest one possible and is called absolute zero. 4. In 848 Lord Kelvin proposed a new temperature scale with being assigned to absolute zero. The size of the degree chosen was the same size as the Celsius degree. Change each of the Celsius temperatures in the table above to degrees Kelvin. Glencoe/McGraw-Hill 4 Algebra: Concepts and Applications

7 7 NAME DATE PERID Stud Guide Pages 96 Writing Equations in Slope-Intercept Form Given the slope m and the -intercept b of a line, the slope-intercept form of an equation of the line is m b. Sometimes it is more convenient to epress the equation of a line in slope-intercept form instead of point-slope form. This form is especiall useful when graphing lines. Eamples: Write the point-intercept form of an equation for each line. a. the line with m and b 4 m b 4 b. the line passing through points at (4, ) and (6, ) m Find m. ( ) m ( 6) Multipl. Add to each side. Simplif. Write the slope-intercept form of an equation for each line, given either the slope and the -intercept or the coordinates of two points.. m, b. m, b 7 4. m, (, ) 4. m, b 6. m, b 6. m, b 7. (, ) and ( 4, ) 8. (, ) and (, ) 9. (, ) and (6, ). (, ) and ( 4, ). (, 4) and (, 6). (, 8) and (, 4). (, 8) and (, 7) 4. (, ) and (6, ) Glencoe/McGraw-Hill 4 Algebra: Concepts and Applications

8 7 NAME DATE PERID Practice Pages 96 Writing Equations in Point-Intercept Form Write an equation in slope-intercept form of the line with each slope and -intercept.. m, b. m 6, b. m 4, b 4. m, b 4. m, b 7 6. m, b m, b 8. m, b 6 9. m, b 9 Write an equation in slope-intercept form of the line having the given slope and passing through the given point.. m, (4, ). m, (, ). m 4, (, 7) 4. m, (, ) 4. m, ( 8, 6). m, (9, 4) 6 6. m, (6, 6) 7. m, ( 8, 7) 8. m, ( 8, 9) Write an equation in slope-intercept form of the line passing through each pair of points. 9. (, ) and (, ). (, ) and (, 4). (, ) and (, 6). (, ) and (6, 6). (4, ) and (, ) 4. (, 6) and ( 4, ). (, ) and (, 6) 6. ( 7, 6) and (, ) 7. (6, 4) and (, ) Glencoe/McGraw-Hill 4 Algebra: Concepts and Applications

9 7 NAME DATE PERID Enrichment Pages 96 Ideal Weight You can find our ideal weight as follows. A woman should weigh pounds for the first feet of height and additional pounds for each inch over feet ( feet 6 inches). A man should weigh 6 pounds for the first feet of height and 6 additional pounds for each inch over feet. These formulas appl to people with normal bone structures. To determine our bone structure, wrap our thumb and inde finger around the wrist of our other hand. If the thumb and finger just touch, ou have normal bone structure. If the overlap, ou are small-boned. If the don t overlap, ou are large-boned. Small-boned people should decrease their calculated ideal weight b %. Large-boned people should increase the value b %. Calculate the ideal weights of these people.. woman, ft 4 in., normal-boned. man, ft in., large-boned. man, 6 ft in., small-boned 4. ou, if ou are at least ft tall Suppose a normal-boned man is inches tall. If he is at least feet tall, then 6 represents the number of inches this man is over feet tall. For each of these inches, his ideal weight is increased b 6 pounds. Thus, his proper weight () is given b the formula 6( 6) 6 or 6 4. If the man is large-boned, the formula becomes 6 4.(6 4).. Write the formula for the weight of a large-boned man in slope-intercept form. 6. Derive the formula for the ideal weight () of a normalboned female with height inches. Write the formula in slope-intercept form. 7. Derive the formula in slope-intercept form for the ideal weight () of a large-boned female with height inches. 8. Derive the formula in slope-intercept form for the ideal weight () of a small-boned male with height inches. 9. Find the heights at which normal-boned males and largeboned females would weigh the same. Glencoe/McGraw-Hill 4 Algebra: Concepts and Applications

10 7 4 NAME DATE PERID Stud Guide Pages 7 Scatter Plots The scatter plot below is a graph of the number of games plaed in the highest-scoring World Cup finals compared to the number of goals scored. The data are listed in the table. Number of Goals Scored Number of Games Plaed Year Number of Number of Games Plaed Goals Scored You can use the scatter plot to draw conclusions about the data. The data points fall roughl along a line with a positive slope. Therefore, we sa there is a positive relationship between the number of games plaed and the number of goals scored. A line with a negative slope would indicate a negative relationship, and no line would indicate no relationship between the variables. A valid conclusion from this scatter plot is that as the number of games plaed increases, more goals are scored. Determine whether each scatter plot has a positive relationship, negative relationship, or no relationship. If there is a relationship, describe it... 8 Number of 6 Cameras Sold 4 Price of Camera 6 Weight (pounds) Height (inches) Length of Swim (meters) 4 Practice per Da (hours) Number of Seeds Sprouted 4 Temperature ( C) Glencoe/McGraw-Hill 44 Algebra: Concepts and Applications

11 7 4 NAME DATE PERID Practice Pages 7 Scatter Plots Determine whether each scatter plot has a positive relationship, negative relationship, or no relationship. If there is a relationship, describe it.. Planetar Data. 8 Diameter 6 (thousands of miles) 4 Rate per Thousand People Marriage Rates Mean Distance from Sun (millions of miles) Year. U.S. Amusement Park Attendance 4. Attendance (,s) 8 6 Water 4 Depth (m) Tsunami Speeds Year Speed (km/h). Heating Costs 6. Monthl Electric Bill ($) Percentage of Crust Common Elements in Earth s Crust 4 6 Temperature ( F) 8 Atomic Number Glencoe/McGraw-Hill 44 Algebra: Concepts and Applications

12 7 4 NAME DATE PERID Enrichment Pages 7 A Scatter Plot Each point on the graph shows the relation between the number of people attending the Ro Cinema and the number of cars in the parking lot. Cars 7 A line is drawn that appears to lie close to most of the points. Here is how to find the equation of this line. Attendance The line passes through (, 4) and (, ). Use the slopeintercept form. m 4 8 m b 4 () b b An equation for the line is. Solve each problem.. Suppose the owner of the Ro decides to increase the seating capacit of the theater to. How man cars should the parking lot be prepared to accommodate?. The points (4, 6) and (4, ) lie on the scatter plot. Write an equation for the line through these points.. Do ou think the equation in Eercise is a good representation of the relationship in this problem? 4. Suppose the equation for the relationship between attendance at the theater and cars in the parking lot is. What might ou suspect about the users of the parking lot? Glencoe/McGraw-Hill 44 Algebra: Concepts and Applications

13 7 NAME DATE PERID Stud Guide Pages Graphing Linear Equations You ma use the slope-intercept form to graph linear equations, as shown in the eample below. Eample: Graph 6. Rewrite in slope-intercept form. 6 6 Subtract from each side. 6 Graph each equation. Divide each side b. To graph, plot a point at the -intercept,. Then use the slope,. From (, ), go down units. Then go right units. Graph a point at (, ). Draw the line through the points (, ) Glencoe/McGraw-Hill 4 Algebra: Concepts and Applications

14 7 NAME DATE PERID Practice Pages Graphing Linear Equations Determine the -intercept and -intercept of the graph of each equation. Then graph the equation Determine the slope and -intercept of the graph of each equation. Then graph the equation Glencoe/McGraw-Hill 4 Algebra: Concepts and Applications

15 7 NAME DATE PERID Enrichment Pages Equations of Lines and Planes in Intercept Form ne form that a linear equation ma take is intercept form. The constants a and b are the - and -intercepts of the graph. a b z In three-dimensional space, the equation of a plane takes a similar form. z a b c z + + = Here, the constants a, b, and c are the points where the plane meets the,, and z-aes. Solve each problem. z. Graph the equation. z z. Graph the equation. 4 z. For the plane in Eercise, write an equation for the line where the plane intersects the -plane. Use intercept forms.. Write an equation for the line where the plane intersects the z-plane. 4. Write an equation for the line where the plane intersects the z-plane. 6. Write an equation for the -plane. 7. Write an equation for the z-plane. 8. Write an equation for a plane parallel to the -plane with a z-intercept of. 9. Write an equation for a plane parallel to the z-plane with an -intercept of. Glencoe/McGraw-Hill 4 Algebra: Concepts and Applications

16 7 6 NAME DATE PERID Stud Guide Pages 6 Families of Linear Graphs Graphs of linear equations that have at least one characteristic in common are called families of graphs. Graphs are families if the have the same slope, the same -intercept, or the same -intercept. An eample of each is shown below. same slope same -intercept same -intercept Eample: Graph the pair of equations. Eplain wh the are a famil of graphs. Since both graphs have the same slope, this is a famil of graphs. Graph each pair of equations. Eplain wh the are a famil of graphs Glencoe/McGraw-Hill 46 Algebra: Concepts and Applications

17 7 6 NAME DATE PERID Practice Pages 6 Families of Linear Graphs Graph each pair of equations. Describe an similarities or differences and eplain wh the are a famil of graphs Compare and contrast the graphs of each pair of equations. Verif b graphing the equations Change so that the graph of the new equation fits each description. 7. same slope, 8. same -intercept, 9. positive slope, shifted down units steeper negative slope same -intercept. same -intercept, less. same slope, shifted. same slope, shifted steep negative slope up 4 units down 6 units Glencoe/McGraw-Hill 46 Algebra: Concepts and Applications

18 7 6 NAME DATE PERID Enrichment Pages 6 Inverse Relations n each grid below, plot the points in Sets A and B. Then connect the points in Set A with the corresponding points in Set B. Then find the inverses of Set A and Set B, plot the two sets, and connect those points. Set A Set B Set A Inverse Set B ( 4, ) (, ) (, ) (, ) (, ) (, ) (, ) (, 4) (, 4) (, ) (, ) (, ) (, ) (, ) (, ) (4, ) Set A Set B Set A Inverse Set B (, ) (, ) (, ) (, ) (, ) (, ) (, ) (, 4) (, ) (, ) (, ) (, ) (, ) (, ) (, ) (4, ) Set A Set B Set A Inverse Set B ( 4, ) (, ) (, ) (, ) (, ) (, ) (, 4) (, ) (, 4) (, ) (, ) (, ) (, ) (, ) (4, ) (,. What is the graphical relationship between the line segments ou drew connecting points in Sets A and B and the line segments connecting points in the inverses of those two sets? Glencoe/McGraw-Hill 46 Algebra: Concepts and Applications

19 7 NAME DATE PERID School-to-Workplace Pages 96 Fied and Marginal Costs (Cost Control Analst) A cost control analzer can estimate the fied cost of production, that is, the cost incurred whether an product is manufactured. The analzer can also estimate the cost of producing each additional item. This cost is called the marginal cost. These two costs combine to indicate the total cost t of producing units. t (marginal cost) () fied cost In the equation above, the marginal cost is the slope of the equation and the fied cost is the -intercept of the equation. If a manufacturer of fire doors sets up an assembl that costs $, to operate and each fire door costs $ to make, describe the total cost of production t in terms of the number of fire doors manufactured. Then graph the equation. t, Cost (in,s) t Units Produced The graph is shown at the right. Given the fied and marginal costs, (a) find an equation for the total cost of production and (b) sketch a graph of the cost equation.. fied cost: $ marginal cost: $. fied cost: $ marginal cost: $ Cost (in s) t Units Produced Cost (in s) t Units Produced. Use the equation in the eample to find the cost of manufacturing 4 fire doors. Glencoe/McGraw-Hill 7 Algebra: Concepts and Applications