F– Direct and Inverse Variation Test Review Alg 1 Name:_________________________________ Date:________________B______________ Given that y varies directly with x, use the specified values to write a direct variation equation that relates x and y. Then find y when x = 2 1. x = 4, y = 12 2. x = 24 y = -6 constant of variation= k = 3 constant of variation= k = ¼ equation: y = 3x equation: y = ¼ x new point: (2,6) new point: (2, ½ ) Given that y varies inversely with x, use the specified values to write an inverse variation equation that relates x and y. Then find y when x = 3. 3. x = 12 y = -2 4. x = 9 y = 4 constant of variation= k = -24 constant of variation= k = 36 equation: y = -24/x equation: y = 36/x new point: (3,-8) new point: (3,12) Given the graphs I, II and III: I. II. 5. Which one(s) show(s) direct variation. Select one answer. A. I only C. II only B. I & II only D. II & III only III. E. III only F. I, II and III Tell whether the table represents direct, inverse or no variation. If it does show variation, write the direct or inverse variation equation. 6. 7. X 2 3 4 5 6 y 6 9 12 15 18 Direct Variation: y = 3x 8. x -1 1 2 3 4 y 12 -12 -6 -4 -3 Inverse Variation: y = -12/x x 5 10 15 20 25 y 75 7.5 5 3.75 3 Neither For #9 & #10, set up an direct or inverse variation equation. Find the constant of variation. Write the equation. Find the new point. 9. The distance traveled in a given time on Interstate 66 varies directly with the speed. Last week we traveled 220 miles at 55 miles per hour. How many miles would we travel in the same time period if we decreased our speed to 50 miles per hour? y = distance, x = speed 220/55 = 4 y = 4x 200 miles 10. The amount of work time in hours (h) needed to prepare for the school play varies inversely with the number of people working (p). Twenty five people working (p) can complete the job in 300 hours (h). Write the inverse variation equation that relates h and p. Then find the how many hours it will take if there are 30 people working. Y= hours, x = people Y = 7500/x 250 hours 11. Does the given chart show direct or inverse variation? Explain why or why not. INVERSE VARIATION- The product of each point is the same (36).