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Vocabulary Tables 100 100 200 Proportions Graphs Y=kx Wild Card 100 100 100 100 200 200 200 200 200 300 300 300 300 300 300 400 400 400 400 400 400 500 500 500 500 500 500 Q: 100 What is an equation that states two ratios are equivalent? Proportion Q: 200 What is the point in the center of a coordinate plane? A: 200 Origin Q: 300 What are the numbers of an ordered pair that locate a point on a coordinate graph? A: 300 Coordinates Q: 400 What is a value that does not change? A:400 Constant Q:500 What is the symbol used to represent a quantity that can change? A:500 Variable Q:100 Does the following table represent a direct variation/prop ortion? X Y 2 4 6 12 4 8 0 0 3 6 A:100 Yes! As the x-values increase, the y-values increase! Hint: You may have to re-order the numbers… but if you move an x, you must move the y as well! Q:200 Complete the following table for 1 y x 2 X y 0 3 6 9 12 A: 200 X 0 3 6 9 12 y 0 1½ 3 4½ 6 Q: 300 Kaden can walk 1 mile in 10 minutes. Create a table of values which represent time and distance. X- Distance Y- Time *Give 4 Coordinates! A: 300 Answers may vary depending on groups! Q: 400 What three characteristics must be true for a table or graph to represent a direct variation? A: 400 1. It is in y=kx form. 2. It always goes through the origin. 3. The constant (k) must be the same! Q: 500 Determine the direct variation/proportion equation for the table shown here. X Y 0 1 2 3 4 0 -3.5 -7 -10.5 -14 A: 500 Y = -3.5x Q: 100 Set- up a proportion and solve the following problem: Johnny scores 27 points on three basketball games. The season has 10 games. How many points can Johnny expect to score by the end of the season? A: 100 27 pts xpts 3 games 10 games 27 10 270 270 3 90 pts ! Q: 200 Set up a proportion and Solve: If y varies directly with x, and y=34 when x=-17. Find x when y=68. A: 200 17 x 34 68 17 68 34* x 1156 34* x 34 x Q: 300 Li mixes 3 units of red paint with 8 units of white paint to get pink. How many units of red paint should she mix with12 units of white paint to get the same pink shade? A: 300 3red x 8white 12 white 3 * 12 = 8 * x 36 = 8 * x 4 ½ units Q: 400 Shane’s neighbor pledged $1.25 for every .5 miles Shane swims in the charity swim-a-thon. If Shane swims 3 miles, how much money will his neighbor donate? A: 400 $7.50 Q: 500 18 45 40 x A: 500 45 * 40 = 18 * x 1800 = 18 * x 100 = x Q:100 If you have a positive constant, your graphed line will be in which two quadrants? A:100 Quadrants I and III Q: 200 What is the point that all direct variation graphs will pass through? A: 200 (0, 0) The origin Q: 300 Determine whether the points given create a direct variation. (1, 3) (2, 6) (3,12) and (4,3) A: 300 No, when you graph the points they do not go through the origin. They also do not have a constant. Q: 400 Determine whether the points given create a direct variation. (2, 9) (3, 13.5) (4, 18) and (5, 22.5) A: 400 Yes, when graphed they go through the origin and have a constant of 4.5. Q: 500 Find an equation and graph the variation where y varies directly as x, when y=3 and x=2. A: 500 y= 1.5x Q:100 X and y vary directly. When x=-15 and y=60. Find the direct variation/proportion equation. A: 100 y= -4x Q: 200 X and y vary directly. When x= 20 and y= 100, find x when y= 500. A: 200 x=100 Q: 300 Why do we say “find an equation which relates x and y”? A: 300 X and y are related by the constant, therefore when we find the direct variation equation/proportion we are finding the link between them. Q: 400 Which of the following is a direct variation equation? a. 17/y=x b. x+2=19 c. x/2=y d. 19-y=x A: 400 C Q: 500 Find the direct variation/proportion equation for the following table. X Y 25 1 50 2 75 3 100 4 125 5 A: 500 y=1/25 x Or Y=.04x Q: 100 True or False: Graphs of Direct Variations/Proportions can start in Quadrant I and end in Quadrant II? A: 100 False Q: 200 Sue gets paid $8 an hour. If she works x hours during the week, write an equation showing how much she will get paid. Let y be that amount (that she gets paid). A: 200 y=$8x Q: 300 Give me two variables which would not represent a direct variation/proportion. Ex. Test grade/# of gallons your mom’s car holds A: 300 Answers may vary! Q: 400 When one variable increases, the other variable ________. When one variable decreases, the other variable ________. A: 400 Increases, Decreases Q: 500 Explain how you know a table of values represents a direct variation/proportion. A: 500 A table which represents a direct variation/proportion will have both x and y values increasing/decreasing. The k’s will also be the same for each set of coordinates.