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1 . Check here " for instructional material to complete this problem. 10- O Graph y = TX Use the graphing tool to graph the equation. 1 x -6 8 1611: Instructional Material Example: Graph y = - zx +5. There are quite a few strategies for graphing lines from an equation. For this example, we will use the slope and the y-intercept to graph the line. First, extract the y-intercept from the linear equation. Since b =5, the y-intercept for this line is (0,5). Plot the y-intercept. Once you have the y-intercept, you can use the slope to locate another point. The slope in this problem is - 5. So, another point will be down 2 units and to the right 3 units. (Remember rise/run.) You can now extend this line using a straightedge.12. Check here12 for instructional material to complete this problem. Let n be the number (in millions) of skateboarders in a country at tyears since 2000. What does the ordered pair (8,16) mean in this situation? Choose the sentence below that best describes what the given ordered pair represents. 0 A. In the year 1992, the number of skateboarders in the country was 16 million. 0 B. In the year 2008, the number of skateboarders in the country was 16 million. 0 C. In the year 2016, the number of skateboarders in the country was 8 million. 12: Instructional Material Print In statistics, we will often study data that come in pairs. It can be helpful to see the paired data on a graph. Each set of paired data can be represented by a point that can be written as (x,y). The points can be plotted on a Cartesian coordinate plane. The origin, or the place where the horizontal (x) and vertical (y) axes intersect, is the starting point. The first value in the paired data (the x-value) will tell you to move left (negative) or right (positive). The second value (the y-value) will place the point up (positive) or down (negative). For example, you can plot the set of paired data (3,5) by counting three units to the right of the origin and up five units. Example: Plot the following paired data. Number of People in a Household (x) Number of TVs in a Household (y) UI AN IN 3 These data can be written as three points (1,2), (2,4), and (3,5). Then, we can plot these three points on the Cartesian plane. As you learn statistics, you will find that most of the data that you will encounter will be positive values. As a result, many times you can limit your Cartesian plane to the first quadrant (the upper right section). Also, there may be times that you will want to change the scale on the axes. Be sure to label your axes with the variables that are being used. Number of TV's Number of People13. Check here's for instructional material to complete this problem. For spring semester 2009, a college charged $40 per unit (credit or hour) for tuition. All students paid a $1 student representation fee each semester. Students who drove to school paid a $50 parking fee each semester. Let T be the total one-semester cost (in dollars) of tuition and fees for a student who drove to school and took u units of classes. Answer parts (a) and (b). a. Find an equation for u and T. [Hint: If there is trouble finding the equation, try creating a table of values for u and T.] The equation that describes the relationship between T and u is T = Simplify your answer. Type an expression using u as the variable.) b. What is the total one-semester cost of tuition and fees for a student who drove to school and took 25 units of classes? $ (Type an integer or a decimal. Do not round.)13: Instructional Material Print You will be studying linear models in great detail in the textbook. For those problems, you will be looking at real data that can sometimes be messy and may best be handled with a calculator. For practice, we will use simplistic models to help prepare you. Example: Find a linear model for the following data for the number of pages in a book and its weight in ounces. Number of Pages Weight (oz.) 150 6 200 8 250 10 300 12 The first thing you may want to do is plot the points to determine whether they fall on a line. 14- Weight (oz.) 175 350 Number of Pages It does appear that the data fall on a line. So, we will use two points to find the slope. 8-6 2 1 m= = 200 - 150 50 25 We now need to find the y-intercept. Since it was not one of the given points, we can substitute any given point for x and y into y = , x + b and solve for b. y= 25 X + b 1 6 = 75 (150) + b 6 = 6+b 0 = b So, the linear model that fits the data is y = = 25 X + 0. Answer: y = 25X14. Check here 14 for instructional material to complete this problem. Let p be the percentage of major firms that t (years) p (percent) perform drug tests on employees and/or job 5 20 applicants at t years since 1980. Some pairs of 8 49 values of t and p are shown in the table to the 10 70 right. 13 77 16 74 (a) Create a graph of the data. 19 67 (b) Are the variables t and p linearly related? 23 62 Explain. 25 71 (a) Choose the correct graph below. O A. O B. O c. OD. Ap 100- 100- 100 TP 100- 80- 80- 80- 80- 60- rcent 60- 60- 60- Percent Percent Percent 40- 540- 40- 40- 20- 20- 20 20- of 10 20 30 10 20 30 10 20 30 10 20 30 Years since 1980 Years since 1980 Years since 1980 Years since 1980 (b) Are the variables t and p linearly related? Explain. O A. Yes because the percentages of firms that perform drug tests over a span of years are described accurately by a nonvertical line. O B. No because the percentages of firms that perform drug tests over a span of years are not described accurately by a nonvertical line.14: Instructional Material In order to determine whether there is a linear relationship between two variables, the first thing you want to do is plot the points to determine whether they fall on a line. You check whether you could draw a straight line that would pass through the points. If you hit all the points with one line, the relationship is perfectly linear. Sometimes the points are really close to a line. In this case, the relationship may be approximately linear. Example: Is a linear model appropriate for the following data for the number of pages in a book and its weight in ounces? Number of Pages Weight (oz.) 150 6 200 8 250 10 300 12 The first thing you want to do is plot the points to determine whether they fall on a line. You check whether you could draw a straight line that would pass through the points. 14- Weight (oz.) 175 350 Number of Pages It does appear that the data fall on a line.15. Check here " for instructional material to complete this problem. a. Plot the data points. Then draw a linear model. Print Let p be the profit (in millions of dollars) of a company for the year that is t years since 2000. Some pairs of values of t and p Choose the correct graph below. are shown in the following table O A. O B. P (years) (millions of dollars) Ap 36- 36- 32 2 28 24 16 10 10 6 12 O C. O D Complete parts a. to d AP Ap 36-KI 36- 10 10 b. Predict when the profit will be $8 million. The profit will be $8 million in the year c. What is the p-intercept of the model? What does it mean in this situation? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. (Type an ordered pair.) O A. The p-intercept of the model is The p-intercept estimates the profit (in millions of dollars) of a company for the year 2000. O B. The p-intercept of the model is The p-intercept estimates the year for which the company has no profit d. What is the t-intercept of the model? What does it mean in this situation? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. (Type an ordered pair.) O A. The t-intercept of the model is The t-intercept estimates the profit (in millions of dollars) of a company for the year 2000. O B. The t-intercept of the model is The t-intercept estimates the year for which the company has no profit.15: Instructional Material In order to determine whether there is a linear relationship between two variables, the first thing you want to do is plot the points to determine whether they fall on a line. You check whether you could draw a straight line that would pass through the points. If you hit all the points with one line, the relationship is perfectly linear. Sometimes the points are really close to a line. In this case, the relationship may be approximately linear. Once you have drawn a linear model, then you can use the line for finding the missing values for data pairs. For instance, if you have a given horizontal value, you can locate that horizontal distance on the line and then look to the vertical axis for the paired vertical-coordinate. You can also locate vertical and horizontal intercepts by locating where the line crosses the respective axis Example: Is a linear model appropriate for the following data for the number of pages in a book and its weight in ounces? Number of Pages Weight (oz.) 150 6 200 8 250 10 300 12 The first thing you want to do is plot the points to determine whether they fall on a line. You check whether you could draw a straight line that would pass through the points. Weight (oz.) 175 350 Number of Pages It does appear that the data fall on a line. You can now use this line to find the missing coordinates for paired data and to find intercepts