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3. 4-3 Writing Rules for Linear Functions

4. Video Tutor Help Writing a rule from wordsWriting a rule from words (4-3) Writing a rule from a tableWriting a rule from a table (4-3) Writing a rule from a graphWriting a rule from a graph (4-3)

5. Video Tutor Help Writing a rule from words Writing a rule from a table Writing a rule from a graph

6. Worksheets 4-3 Note-Taking Guide 4-3 Practice 4-3 Guided Problem Solving

7. Vocabulary Practice Chapter 4 Vocabulary (Electronic) Flash Cards

8. Additional Lesson Examples 4-3 Step-by-Step Examples

9. Lesson Readiness 4-3 Problem of the Day 4-3 Lesson QuizCurrently not available

10. Graphing Linear Functions LESSON 4-2 Time (min) Height (ft) 0 150 1 155 2 160 1.A rock climber 150 ft above the base of a cliff climbs at a rate of 5 ft per min. Make a table to describe the climber’s height above the cliff base as a function of elapsed time. Graph the function. 2.Graph the function y = –3x – 4. Lesson Quiz

11. Graphing Linear Functions 3.One kilogram is equivalent to about 2.2 pounds. The weight of an object in pounds is a function of its weight in kilograms. Make a table and graph the function. LESSON 4-2 Kilograms (kg) Pounds (lb) 0000 1 2.2 3 6.6 2 4.4 Lesson Quiz

16. Example 7-1a Write an equation in slope-intercept form for the line. Slope-intercept form Answer: Replace m with and b with 7. Write Equations From Slope and y-Intercept

17. Example 7-1a Write an equation in slope-intercept form for the line. Replace m with 0 and b with –3. Answer: Simplify. Slope-intercept form Write Equations From Slope and y-Intercept

18. Example 7-1a Write an equation in slope-intercept form for the line. Slope-intercept form Replace m with 2 and b with 0. Answer: Simplify. Write Equations From Slope and y-Intercept

19. Example 7-2a Write an equation in slope-intercept form for the line graphed. The y -intercept is –4. From (0, –4), you can go up one unit and to the right one unit to another point on the line. So, the slope is 1. Write an Equation From a Graph

20. Example 7-2a Slope-intercept form Replace m with 1 and b with –4. Answer: Simplify.

21. Example 7-4a Write an equation for the line that passes through (7, 0) and (6, 3). Step 1Find the slope m. Definition of slope Write an Equation Given Two Points

22. Example 7-4a Step 2Find the y -intercept b. Use the slope and the coordinates of either point. Slope-intercept form Replace m with –3, x with 7, and y with 0. Simplify. Pick a given point (7,0)

23. Example 7-4a Step 3Substitute the slope and y -intercept. Replace m with –3 and b with 21. Answer: Slope-intercept form

24. Example 7-5a Use the table of values to write an equation in slope- intercept form. xy –216 –110 04 1–2 Definition of slope Step 1Find the slope m. Use the coordinates of any two points. Write an Equation From a Table

25. Example 7-5a Step 2Find the y -intercept b. Use the slope and the coordinates of either point. Slope-intercept form Replace m with –6, y with 16, and x with –2. Simplify. Step 3Substitute the slope and y -intercept. Answer: Slope-intercept form Replace m with –6 and b with 4. Pick a given point (-2,16)

27. A rate for Internet access is $15 per month plus $.25 per hour of use. Write a function rule that shows how the monthly bill depends on the number of hours used. Writing Rules for Linear Functions LESSON 4-3 y = 15 + 0.25x The function rule y = 15 + 0.25x shows the monthly bill for x hours of use. Wordsmonthly bill = $15 + $.25 number of hours Let x y = the number of hours. = the monthly bill. Function y = 15 + 0.25 x Additional Examples

30. Do the data in the table below represent a linear function? If so, write a rule for the function. Writing Rules for Linear Functions LESSON 4-3 Since each ratio is the same, the function is linear. Use slope-intercept form to write a function rule. Find the changes in inputs. Find the changes in outputs. Compare the changes as ratios. Change in y Change in x 2121 2121 2121 2121 Additional Examples

31. (continued) Writing Rules for Linear Functions LESSON 4-3 According to the table, the point (0, 8) lies on the graph of the function. So the y- intercept is 8. The slope is 2. y = 2x + 8 Substitute 2 for m and 8 for b. Additional Examples

34. Find the equation of the line in the graph below. Writing Rules for Linear Functions LESSON 4-3 Step 1 Find the slope. Use the points (–4, 0) and (0, 8). The y-intercept is 8. slope = = 2 8 – 0 0 – (–4) Step 2 Use the slope and one point to write an equation. y – y 1 = m (x – x 1 ) y – 0 = 2 [x – (–4)] y = 2 (x + 4) Use the point (–4,0) for (x 1, y 1 ). Using the point (–4, 0), the equation of the line is y = 2(x + 4), or y = 2x + 8. Additional Examples