2. A proportion is an equation stating that two ratios are equal.

3. A proportional relationship can exist between 2 or more sets of numbers if a proportion can be written. Example: (2,4,10) and (4,8,20) are proportional because. A nonproportional relationship exists between sets of numbers when a proportion or extended proportional with equal ratios cannot be written. Example: (1,3,5) and (3,6,9) are nonproportional because.

4. Examine the table shown below. Determine whether the relationship between the x and y values in the table is proportional. If it is, write a rule that expresses the relationship. xy 13 26 39 412 For each row of values, write a ratio using y as the numerator and x as the denominator. Compare the ratios. Are they equivalent? If so, then they are proportional. Write a rule to solve for y. Hint: It’s just like writing an expression for the nth term.

5. Examine the table shown below. Determine whether the relationship between the x and y values in the table is proportional. If it is, write a rule that expresses the relationship. xy 12 24 37 410 For each row of values, write a ratio using y as the numerator and x as the denominator. Compare the ratios. Are they equivalent? If so, then they are proportional. Write a rule to solve for y. Hint: It’s just like writing an expression for the nth term.

6. Examine the table shown below. Determine whether the relationship between the x and y values in the table is proportional. If it is, write a rule that expresses the relationship. xy 14 28 312 416 For each row of values, write a ratio using y as the numerator and x as the denominator. Compare the ratios. Are they equivalent? If so, then they are proportional. Write a rule to solve for y. Hint: It’s just like writing an expression for the nth term.

7. Examine the table shown below. Determine whether the relationship between the x and y values in the table is proportional. If it is, write a rule that expresses the relationship. xy 14 27 310 413 For each row of values, write a ratio using y as the numerator and x as the denominator. Compare the ratios. Are they equivalent? If so, then they are proportional. Write a rule to solve for y. Hint: It’s just like writing an expression for the nth term.

8. This was your rule from the first problem. It is both linear and proportional. A Linear Equation is an equation whose graph in a coordinate plane is a straight line. It is stated in the form, where k and b are constant.

9. This was your rule from the first problem. It is both linear and proportional. If the linear equation does NOT have a b, (b=0),then we say the linear equation is proportional, and k becomes the constant of proportionality. We also call the proportional equation a direct variation. When we graph a direct variation, the line will go through the origin (0,0).

10. x3x3xy 0 1 2 Let’s use the rule to prove direct variation. Plug in the given x values to find y and then graph the points.

11. y = 3x – 5 y = ¼ x + 6 y =.5x + 2 y = 8x - 2 y = - ½ x + ½ y = -18x - 8 y = 12x + 3 y = -5x + 1/4 These are all examples of linear equations, y=kx+b, but NOT direct variations, y=kx.

12. y = 3x y = ¼ x y =.5x y = 8x y = - ½ x y = -18x y = 12x y = -5x These are all examples of linear equations, y=kx+b, AND direct variations, y=kx.

13. direct variation not a direct variation When b=0, the equation simplifies to y=kx. Then y is said to be proportional to x, and the constant k is called the constant of proportionality. y=kx is also known as a direct variation, which means that when graphed, the line goes directly through the origin.

14. XY 01 13 25 37 What is the rule for y? Is it linear? Is it a direct variation, or proportional?

15. XY -2 00 12 24 What is the rule for y? Is it linear? Is it a direct variation, or proportional?

16. XY -21 00 2 4-5 What is the rule for y? Is it linear? Is it a direct variation, or proportional?

17. 8.4A Generate a different representation of data given another representation of data (such as a table, graph equation, or verbal description).

18. Any relationship between two variables can usually be represented in several ways. Equation: 2n-1=p Table nP -4-7 0 59 Graph Verbal Description The value of p is 1 less than twice the value of n.

19. Example: A medication is administered in a dosage (d) of 4 milligrams per kilogram of body weight (w). What equation would be used to find the weight of a person whose dosage is 240 milligrams? To solve this equation, you would divide both sides by 4, and your answer would be 60 kilograms. Fill in the known dosage to obtain the desired equation. Write the equation.

20. The table shows some equivalent temperatures in Fahrenheit and degrees Celsius. Draw a graph and represent the same linear relationship. x (°C)-20010 y (°F)-43250

21. Which equation describes the linear relationship shown in the table? x4610 y764

22. Which ordered pair does NOT lie on the graph? A (-6, -5)B (-2, -1)C (2, 1)D (3,4)

23. The students in Mr. Lee’s science class are ordering the materials they will need for a science experiment. Each student will need a bag of plant seeds that costs $1.00 and a 6-plant tray that costs $2.50. If x represents the number of students in Mr. Lee’s science class, which equation can be used to find y, the amount in dollars spent by Mr. Lee’s students? A y = 2.5x + 1 B y = 3.5x C y = x + 3.5 D y = x + 2.5

24. Which table of values best represents ordered pairs on the graphed equation? The graph of the equation y = 2x+5 is shown at the right. xy 0 5 -4-3 2 1 xy 1 7 -5 -2 1 xy 0 5 -6-7 -2 9 xy 3 0-5 -7-8 ABCD

26. A fast train, known as a bullet train, travels at an average speed of 163 miles per hour. The equation below shows the relationship between d, the number of miles the train travels, and t, the number of hours it travels. d = 163t What is the distance in miles the train will travel in 1½ hours?

27. A baseball card was worth $3 when it was issued in 1996. The table shows the value of the card each year since 1996. Based on the information in the table, what is a reasonable prediction for the value of the baseball card in 2004? F Between $5 and $6 G Between $6 and $7 H Between $7 and $8 J Between $8 and $9

28. A cell phone service provider charges $9.95 for the first 60 minutes of use each month and $0.10 for each additional minute. Which equation can be used to calculate c, a customer’s total cost when the cell phone is used more than 60 minutes in a month, if t represents the time in minutes?

29. The table below shows land-speed records. Whose land-speed record did Green exceed by exactly 368.84 miles per hour? A Elyston B Cobb C Breedlove D Noble

30. The equation is used to calculate the total cost, c, of renting a canoe for h hours. What will be the cost of renting a canoe for 5 hours? A $125B $150 C $100D $40