Mass = Density Volume; and Volume of model / Volume of miniature = (H of model / H of miniature)3.

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1 Problem-of-the-Week The Problem: Miniature Amateurs Mr. Ellis Hackworth has a miniature Pramid of Egpt. It is inches in height. Mr. Hackworth was invited to displa it at an ehibition. Mr. Hackworth felt it was too small and decided to build a scaled-up model of the Pramid out of material whose densit is ( / ) times the densit of the material used for the miniature. He did a "back-of-the-envelope" calculation to check whether the model would be big enough. If the mass (or weight) of the miniature and the scaled-up model are to be the same, how man inches in height will be the scaled-up Pramid? Give our answer to two places of decimal. It is important to note that Mass = Densit Volume; and Volume of model / Volume of miniature = (H of model / H of miniature). In the above equation, H is the characteristic dimension (sa, height). If the mass is to be the same, then densit is inversel proportional to volume. The volumes are directl proportional to the cubes of the heights for objects that are geometricall similar. Therefore, the heights are seen to be inversel proportional to the cube roots of the densities. Thus, Height of model = Height of miniature (Densit of miniature / Densit of model)/ RAISING THE BAR ***Guess the the problem of the week ACCURATELY b Frida, November 9th and our name will be included in the weekl raffle for a cand bar. Each Scholar onl gets NE submission.**** GD LUCK!

2 -8 NAME Stud Guide Direct and Inverse Variation If two variables and are related b the equation k, where k is a nonzero constant, then the equation is called a direct variation, and k is called the constant of variation. If two variables and are related b the equation k, where k 0, then the equation is called an inverse variation. DATE Student Edition Pages 9 Eample : If varies directl as, and Eample : If varies inversel as, and when, find when, find when 7. when. k k k k k (7) () k k k k 9 Solve. Assume that varies directl as.. If when, find. If 9 when, find when. when.. If when, find. If when, find 8 when. when. Solve. Assume that varies inversel as.. If 9 when 7, find. If. when.9, find when. when If when, find 8. If when, find when. when. Glencoe/McGraw-Hill Algebra

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4 - NAME Stud Guide Graphing Linear Equations There are three methods ou can use for graphing equations. You can find two ordered pairs that satisf the equation, the - and -intercepts, or the slope and -intercept. DATE Student Edition Pages Eample : Graph 0 b using the - and -intercepts. The equation is in standard form A B C. C The -intercept is, or. A C The -intercept is, or. B Thus, the graph contains the points (, 0) and (0, ). Eample : Graph b using the slope and -intercept. The -intercept is, the slope. Graph each equation b using the - and -intercepts... 7 (0, ) (0, ) 0 (, 0) Graph each equation b using the slope and -intercept... Glencoe/McGraw-Hill Algebra

5 - NAME Practice Graphing Linear Equations Graph each equation b using the - and -intercepts... DATE Student Edition Pages.. Graph each equation b using the slope and -intercept... Glencoe/McGraw-Hill Algebra

6 7-8 NAME Stud Guide Graphing Inequalities in Two Variables DATE Student Edition Pages = + > + The graph of the equation is a line that separates the coordinate plane into two regions. Each region is called a halfplane. The line for is called the boundar for each half-plane. The boundar line in both regions is the line for. In, the boundar is not part of the graph. The boundar is shown as a dashed line. All points above the line are part of the graph. This graph is called an open half-plane. In, the boundar is part of the graph and is shown as a solid line. The graph also contains all points below the line. This graph is called a closed half-plane. Graph each inequalit Glencoe/McGraw-Hill Algebra

7 7-8 NAME Practice Graphing Inequalities in Two Variables DATE Student Edition Pages Shade the appropriate half-plane to complete the graph of each inequalit.... Graph each inequalit Glencoe/McGraw-Hill Algebra

8 Topic Quiz: The Slope of a Line NAME Find the slope of the line. Write our answer in simplest form..... (, ) (0, ) (, ) (, ) (, ) (, ) (, ) (, ) m m m m The slope of a drivewa should be no more than 0. The diagram shows a drivewa.. Find the slope of the drivewa. Write our answer in simplest form. The slope of the drivewa is.. Is the slope of the drivewa acceptable? Circle es or no. es no 0 8 (, 0) (08, ) Topic Quiz: Direct Variation The variables and var directl. Write an equation that relates and.. 8 and 7. and 8 00 Meridian Creative Group, a Division of Larson Tets, Inc.. 7and 7. and 8. You pa $0. for gallons of gasoline. Use a direct variation model that relates the total price P to the number of gallons of gasoline g to find how much ou would pa for. gallons of gasoline. You would pa $ for. gallons of gasoline.. The length of our hair varies directl with the time. The longest hair on record belongs to Hoo Sateow of Thailand. His hair grew to 0 inches over a 8-ear period. Use a direct variation model that relates the length L of his hair to the ears to find how long his hair would be after 7 ears. Round our answer to the nearest inch. His hair would be inches long. -0/7-0 Graphing Linear Equations 9

9 Topic Quiz: Graphing Horizontal and Vertical Lines Graph the equation of the line. NAME.... The map shows the latitude and longitude lines near Santiago, Chile. Write equations for the latitude and longitude lines that describe the location of Santiago.. Latitude line equation:. Longitude line equation: PACIFIC CEAN Valparaíso San Antonio Santiago Cruz CHILE S S ARGENTINA 7 W Curicó 7 W 70 W S 9 W Topic Quiz: Graphing Lines Using Intercepts Use the -intercept and -intercept to graph the equation of the line Meridian Creative Group, a Division of Larson Tets, Inc. 8 8 A compan wants to make a profit of $00 selling skateboards and in-line skates. The compan makes $ profit on each skateboard and $0 profit on each pair of in-line skates. This is modeled b the equation 0 00, where is the number of skateboards and is the number of pairs of in-line skates.. Find the -intercept and -intercept of the line. The -intercept is. The -intercept is.. Graph the model. 8 Inline skates sold Skateboards sold /7-0 Graphing Linear Equations 8

10 - NAME Stud Guide Writing Linear Equations in Slope-Intercept Form The -coordinate of the point where a line crosses the -ais is called the -intercept. Similarl, the -coordinate of the point where the line crosses the -ais is called the -intercept. If an equation is given in standard form A B C and B is A C not zero, the slope of the line is and the -intercept is. B B C The -intercept is where A 0. A Eample: Find the - and -intercepts of the graph of 0. Then write the equation in slopeintercept form. Since A, B, and C 0, C 0 C 0 A m A B B Thus, the -intercept is, and the -intercept is. The equation of the line in slope-intercept form is. Find the - and -intercepts of the graph of each equation Write an equation in slope-intercept form of a line with the given slope and -intercept. Then write the equation in standard form.. m, b 0. m, b 0 7. m, b 8. m, b Find the slope and -intercept of the graph of each equation. Then write each equation in slope-intercept form DATE Student Edition Pages Slope-Intercept Form of a Linear Equation Given the slope m and the -intercept b of a line, the slope-intercept form of an equation of the line is m b Glencoe/McGraw-Hill Algebra

11 Graphing was Name Pd Graph each of the following equations on the graph below and label the equation. Check our answer with a graphing calculator.. Graph using = m + b. a) = - m = b = b) = + m = b = Y c) = - + m = b = X d) = - - m = b =. Graph using - and -intercepts. a) + = -int: -int: Y b) - = -8 -int: c) - + = - -int: d) - - = -int: -int: -int: -int: X. Graph using a table. a) = b) + = Y X

12 Graphing Applications Name For each of the equations, answer the following questions. ) The librar charges 0 a week for a late book. a) Write an equation for total fee. b) Define the variables: X = Y = c) Find the - and -intercept. -int: Y -int: d) Complete the table and graph. X e) What is the slope of the line? M = SLPE = RISE RUN = f) Does the graph increase or decrease? ) Flowers are $ each with a $ deliver charge. a) Write an equation for total fee. b) Define the variables: X = Y = c) Find the - and -intercept. -int: Y -int: d) Complete the table and graph. X e) What is the slope of the line? M = SLPE = RISE RUN = f) Does the graph increase or decrease?