1. example 6 Criminal Sentences Chapter 2.1 The function describes the mean time y served in prison for a crime as a function of the mean sentence length x, where x and y are each measured in months. To find the sentence for a crime that would give an expected time served of 10 years, write an equation and solve it by using a.the x-intercept method, and b.the intersection method.  2009 PBLPathways

2. The function describes the mean time y served in prison for a crime as a function of the mean sentence length x, where x and y are each measured in months. To find the sentence for a crime that would give an expected time served of 10 years, write an equation and solve it by using a.the x-intercept method, and b.the intersection method.

3.  2009 PBLPathways The function describes the mean time y served in prison for a crime as a function of the mean sentence length x, where x and y are each measured in months. To find the sentence for a crime that would give an expected time served of 10 years, write an equation and solve it by using a.the x-intercept method 10 years = 120 months mean sentence length mean time in prison

4.  2009 PBLPathways The function describes the mean time y served in prison for a crime as a function of the mean sentence length x, where x and y are each measured in months. To find the sentence for a crime that would give an expected time served of 10 years, write an equation and solve it by using a.the x-intercept method 10 years = 120 months mean sentence length mean time in prison

5.  2009 PBLPathways The function describes the mean time y served in prison for a crime as a function of the mean sentence length x, where x and y are each measured in months. To find the sentence for a crime that would give an expected time served of 10 years, write an equation and solve it by using a.the x-intercept method 10 years = 120 months mean sentence length mean time in prison

6.  2009 PBLPathways The function describes the mean time y served in prison for a crime as a function of the mean sentence length x, where x and y are each measured in months. To find the sentence for a crime that would give an expected time served of 10 years, write an equation and solve it by using a.the x-intercept method 10 years = 120 months mean sentence length mean time in prison

7.  2009 PBLPathways The function describes the mean time y served in prison for a crime as a function of the mean sentence length x, where x and y are each measured in months. To find the sentence for a crime that would give an expected time served of 10 years, write an equation and solve it by using a.the x-intercept method 10 years = 120 months mean sentence length mean time in prison

8.  2009 PBLPathways The function describes the mean time y served in prison for a crime as a function of the mean sentence length x, where x and y are each measured in months. To find the sentence for a crime that would give an expected time served of 10 years, write an equation and solve it by using a.the x-intercept method 10 years = 120 months mean sentence length mean time in prison

9.  2009 PBLPathways The function describes the mean time y served in prison for a crime as a function of the mean sentence length x, where x and y are each measured in months. To find the sentence for a crime that would give an expected time served of 10 years, write an equation and solve it by using a.the x-intercept method 10 years = 120 months mean sentence length mean time in prison

10.  2009 PBLPathways The function describes the mean time y served in prison for a crime as a function of the mean sentence length x, where x and y are each measured in months. To find the sentence for a crime that would give an expected time served of 10 years, write an equation and solve it by using a.the x-intercept method 10 years = 120 months mean sentence length mean time in prison

11.  2009 PBLPathways The function describes the mean time y served in prison for a crime as a function of the mean sentence length x, where x and y are each measured in months. To find the sentence for a crime that would give an expected time served of 10 years, write an equation and solve it by using a.the x-intercept method 10 years = 120 months mean sentence length mean time in prison

12.  2009 PBLPathways The function describes the mean time y served in prison for a crime as a function of the mean sentence length x, where x and y are each measured in months. To find the sentence for a crime that would give an expected time served of 10 years, write an equation and solve it by using a.the x-intercept method 10 years = 120 months mean sentence length mean time in prison

13.  2009 PBLPathways The function describes the mean time y served in prison for a crime as a function of the mean sentence length x, where x and y are each measured in months. To find the sentence for a crime that would give an expected time served of 10 years, write an equation and solve it by using a.the x-intercept method 10 years = 120 months mean sentence length mean time in prison

14.  2009 PBLPathways The function describes the mean time y served in prison for a crime as a function of the mean sentence length x, where x and y are each measured in months. To find the sentence for a crime that would give an expected time served of 10 years, write an equation and solve it by using a.the x-intercept method 10 years = 120 months mean sentence length mean time in prison

15.  2009 PBLPathways The function describes the mean time y served in prison for a crime as a function of the mean sentence length x, where x and y are each measured in months. To find the sentence for a crime that would give an expected time served of 10 years, write an equation and solve it by using a.the x-intercept method 10 years = 120 months mean sentence length mean time in prison

16.  2009 PBLPathways The function describes the mean time y served in prison for a crime as a function of the mean sentence length x, where x and y are each measured in months. To find the sentence for a crime that would give an expected time served of 10 years, write an equation and solve it by using a.the x-intercept method 10 years = 120 months mean sentence length mean time in prison (223.43, 0)

17.  2009 PBLPathways The function describes the mean time y served in prison for a crime as a function of the mean sentence length x, where x and y are each measured in months. To find the sentence for a crime that would give an expected time served of 10 years, write an equation and solve it by using b.the intersection method

18.  2009 PBLPathways The function describes the mean time y served in prison for a crime as a function of the mean sentence length x, where x and y are each measured in months. To find the sentence for a crime that would give an expected time served of 10 years, write an equation and solve it by using b.the intersection method

19.  2009 PBLPathways The function describes the mean time y served in prison for a crime as a function of the mean sentence length x, where x and y are each measured in months. To find the sentence for a crime that would give an expected time served of 10 years, write an equation and solve it by using b.the intersection method

20.  2009 PBLPathways The function describes the mean time y served in prison for a crime as a function of the mean sentence length x, where x and y are each measured in months. To find the sentence for a crime that would give an expected time served of 10 years, write an equation and solve it by using b.the intersection method

21.  2009 PBLPathways The function describes the mean time y served in prison for a crime as a function of the mean sentence length x, where x and y are each measured in months. To find the sentence for a crime that would give an expected time served of 10 years, write an equation and solve it by using b.the intersection method (223.43, 120)

22.  2009 PBLPathways Enter the Equation 1.Use the  key to enter the function as Y1. 2.Make sure that all other functions and plots are turned off. Set the Window 3.Use the  key to set the window as shown. 4.Set Xscl =50 and Yscl =20.

23.  2009 PBLPathways Find the x-intercept 5.Press   to access CALC. A CALCULATE screen appears. 6.Press the  key or cursor down to 2: zero and press . 7.You are brought back to the graph screen. 8.You must select a Left Bound to tell the calculator where to look for the x- intercept. To do this, move the cursor somewhere close to the left side of the x-intercept. Press .

24.  2009 PBLPathways 9.Notice that an arrow appears at the top of the screen above your left bound. This is the left bound of the interval that contains the x-intercept. 10.You must select a Right Bound to tell the calculator where to look for the x- intercept. To do this, move the cursor somewhere close to the right side of the x-intercept. Press . 11.Notice that an arrow appears at the top of the screen above your right bound. This is the right bound of the interval that contains the x-intercept.

25.  2009 PBLPathways 12.Next, you must enter a Guess. You can enter a value somewhere within the interval defined by your left and right bounds. However, you can just press . 13.Finally, press  to see the coordinates of the x-intercept at the bottom of the screen.

26.  2009 PBLPathways Enter the Equation 1.Use the  key to enter the left side of the function as Y1 = 120 and the right side of the function as Y2 = 0.55x – 2.886. Set the Window 2.Use the  key to set the window as shown. 3.Set Xscl = 50 and Yscl = 20.

27.  2009 PBLPathways Graph the equations 4.Press the  key to see the graphs. 5.Press  to see the equation of one of the lines. Use the up or down arrow to see the equation of the second line. 6.Use the right arrow  key to get close to the intersection point of the two lines. Note that using  does not necessarily give the exact coordinates of the intersection point.

28.  2009 PBLPathways Find the exact coordinates of the Intersection point 7.Press   to access CALC. A CALCULATE screen appears. 8.Press the  key or cursor down to 5: intersect and press . 9.You are brought back to the graph screen.

29.  2009 PBLPathways 10.You must select a First curve to tell the calculator which of the lines you want to use for the intersection. Press . 11.Next you must select a Second curve to tell the calculator which second curve to use for the intersection. Use the up or down arrow key to move to the other line. Press . 12.Next, you must enter a Guess. You can enter a value or use the arrow keys to move close to the point of intersection. 13.Finally, press  to see the coordinates of the Intersection at the bottom of the screen.