MS Algebra A-F-IF-7 Ch. 6.3b Solving Real World Problems with the Point-Slope Form

Transcription

1 MS Algebra A-F-IF-7 Ch. 6.3b Solving Real World Problems with the Point-Slope Form ALGEBRA SUPPORT (Homework) Solving Problems by Writing Equations in Point-Slope Form

2 Title: 6.3b Apply Point-Slope Form to Solve Real World Problems Date: SUPPORT Learning Target By the end of the period, I will apply the point-slope form to write equations and solve real world problems. I will demonstrate this by completing Four- Square Notes and by solving problems in a pair/group activity.

3 Home Work 1-2-3: 1) Class 4-Square Notes Put In Binder? 2) Section 6.3 Pg ) Section TxtBk.Prob.#45-49 ALL Notes Copied on blank sheet Solved and Put in Binder? of paper in Binder? Table of Contents Date Description Date Due

4 Notes: How To Get To Point-Slope Form Step 1) Plug m and one point into x y y Y 1 = m(x X 1 ) X 1 Y 1 Step 2) Solve for y (if you want slope-intercept form)

5 HW # 45 Solve a multi-step problem TELEVISION In order to use an excerpt fro a movie in a new television show, the television producer must pay the director of the movie $790 for the first 2 minutes of an excerpt and $130 per minute after that. A) Write an equation that gives the total cost (in dollars) of using the excerpt as a function of the length (in minutes) of an excerpt that is 2 minutes long or longer. B) Find the total cost of using an excerpt that is 8 minutes long.

6 HW #46 Write a real-world linear model from a table Internet Services A school district pays an installation fee and a monthly fee for Internet service. The table shows the total cost of Internet service for the school district over different numbers of months. Explain why the situation can be modeled by a linear equation. What is the installation fee? What is the monthly service fee? Months of Service Total Cost (dollars) 9,378 12,806 16,234 19,662 23,090 26,518 We can make a linear equation because

7 HW #46 Continued Write a real-world linear model from a table Internet Services A school district pays an installation fee and a monthly fee for Internet service. The table shows the total cost of Internet service for the school district over different numbers of months. Explain why the situation can be modeled by a linear equation. What is the installation fee? What is the monthly service fee? Months of Service Total Cost (dollars) 9,378 12,806 16,234 19,662 23,090 26,518 Equation: Installation Fee: Monthly Service Fee:

8 Storm Check (Think, Write, Discuss, Report) If you are given the slope and one point, how can you create a linear equation that is in point-slope form? (2-3 sentences) When given the slope and one point, I can create a linear equation in point-slope form by.

9 Step 3) Solve for y (if you want slope-intercept form) Notes: How To Get To Point-Slope Form Step 1) Make a table Use the two points to calculate SLOPE (m) m = Y 2 Y 1 X 2 X 1 x y X 1 Y 1 X 2 Y 2 Step 2) Plug m and one point into y Y 1 = m(x X 1 )

10 HW #47 Multiple Choice During the period , the annual sales of a small company increased by $10,000 per year. In 1997 the annual sales were $97,000. Which equation gives the annual sales S (in dollars) as a function of the time T (in years) since 1994? (SHOW YOUR WORK!) A) S = 10,000T + 97,000 B) S = 10,000T + 100,000 C) S = 10,000T + 67,000 D) S = 10,000T 3,000

11 HW # 48 Solve a multi-step problem TRAFFIC DELAYS From 1996 to 2003 in San Diego, California, the annual excess fuel (in gallons per person) consumed due to traffic delays increased by about 1.3 gallons per person each year. In 1999 each person consumed about 15 gallons of excess fuel. A) Write an equation that gives the annual excess fuel (in gallons per person) as a function of time (in years) since B) How much excess fuel was consumed per person in 2001?

12 HW # 49 MARATHON The table below shows a marathon runner s speed at several outdoor temperatures. Write a equation in point-slope form that relates running speed (in feet per second) to temperature (in degrees Fahrenheit). Estimate the runner s speed when the temperature is 80⁰F? Temperature (⁰F) Running Speed (ft/sec) ???

13 Storm Check (Think, Write, Discuss, Report) If you are given a table of data points, how can you determine if you can use a linear equation to model the situation? (2-3 sentences) When given a table of data points, I can determine if I can use a linear equation to model the situation by.

14 Vocabulary 1) Slope 2) y-intercept 3) Data Pair 4) Slope-Intercept Form 5) Point-Slope Form