Direct Variation notes. Direct. Variation. 8th Grade Math
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1 Direct Variation 8th Grade Math 1
2 TEKS for the Day 2
3 Essential Question(s) How can solution meaning be derived from an equation or inequality in a problem situation? 3
4 Direct Variation Vocabulary Review an equation of the form that describes proportional situations. Independent Variable The variable in a relationship that remains constant. Dependent Variable The variable that changes based on the value of the independent variable. Constant of Proportionality, k the constant ratio of the dependent variable to the independent variable in a proportional linear relationship; 4
5 WARM-UP The Papyrus Print Shop can print 1750 posters in 5 hours. How many posters can they print per hour? a. Create a word ratio for this situation. b. Determine the rate for this relationship. posters per hours c. Predict the number of posters the Papyrus Print Shop can print in 8 hours. Multiply the rate (posters in one hour) by the number of hours. posters 5
6 Student Notes Problem 1: The Parchment Print Shop can print 3150 posters in 7 hours. How many posters can they print per hour? A. Underline and label the independent and dependent variables. Time determines the number of posters printed. Time is the independent variable and posters is the dependent variable. B. What is the constant of proportionality, or k, for this situation? Words: Numbers (k): posters per hour k = 450 C. Write an equation using k that represents this situation. y=450x, so D. If The Parchment Print Shop is printing at the same rate, how many posters can they print in 12 hours? y=450x y=450(12) y = 5400 posters 6
7 Problem 2: Myka is training for a marathon. Her distance varies directly as the time as listed in the table below. How far does Myka run in 1 hour? A. Underline and label the independent and dependent variables. Time determines the number of miles that Myka runs. Time is the independent variable and miles is the dependent variable. B. What is the constant of proportionality, k, for this situation? Words: Numbers (k): miles per hour k = 5.2 C. Write an equation using k that represents this situation. y = 5.2x, so D. If Myka runs at the same rate throughout her training, how long will it take her to run 26 miles? y = 5.2x 26 = 5.2x y = 5 hours 7
8 Steps for solving direct variation: 1. Solve for k. 2. Write the equation using. 3. Solve for the missing value. * If the missing value is x, divide y by k. * If the missing value is y, multiply the numbers. 8
9 I DO: 3. Use the table to answer the questions below. A. Find the constant of proportionality, k. k = 3 5 or 0.6 B. If x is 47, what is y? y = or
10 you DO: 4. If y is directly proportional to x, and y is 8 when x is 10. A. Find k. k = 0.8 or 4 5 B. Write the direct variation equation that represents this situation. y = 0.8x or y = 4 5 x C. Find the value of x when y is. x = 7 10
11 Complete 5 & 8 with a partner: 5. The number of centimeters in a measure varies directly as the number of inches. A. What is k for this situation? k = 2.54 B. Write the direct variation equation that represents this situation. y = 2.54x C. Find the measure of an object in centimeters that is 50 inches long. y = 2.54(50) y = 127 cm 11
12 I DO: 6. Daniel ran 9.75 miles in 1.5 hours Monday and 19.5 miles in 3 hours Thursday. A student did the following to find the distance Daniel could run in 4 hours. Is he correct? If not, explain and correct the error. y=kx y=9.75(4) y=39 miles He found k incorrectly. k=6.5 Should be: y=kx y=6.5(4) y=26 miles 12
13 I DO: 7. The number of miles a car can travel is directly proportional with the number of gallons of gas in its tank. Oliver can travel 399 miles with 19 gallons of gas in his car. A. What is k for this situation? k=21 B. Write the direct variation equation that represents this situation. y=21x C. If he drove 189 miles, how many gallons did he have in his car? 189 = 21x x = 9 gal 13
14 8. The number of kilograms of water in a person s body varies directly as the person s mass. A person with a mass of 90 kg contains 60 kg of water. How many kilograms of water are in a person whose mass is 50 kg? = kg of water mass = 60 kg 90 kg k = 2 3 y = 2 3 x y = 2 3 (50) y = kg 14
15 exit Ticket: 1. The number of words Sam can type varies directly with the time he spends typing. Sam can type 280 words in 8 minutes. A. Find the constant of proportionality. k=35 B. If Sam types for an hour and a half, how many words would you expect him to type? x = 3150 words 2. The number of rungs on a tree s trunk, r, is directly proportional to the tree s age, a. If a 27 year old tree has 18 rings on its trunk, how many rings would you expect a 63 year old tree to have? r = 42 rings 15
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