Name ______________________________ Date ______________ Period ______ IP#3-­‐6: DIRECT VARIATION 1. Use proper grammar and punctuation to write a definition of direct variation in your own words. Find the constant of variation and then write the equation that expresses the variation. 2. 𝑦 varies directly as 𝑥 and 𝑦 = 8 when 𝑥 = 12 3. 𝑦 varies directly as 𝑥 and 𝑦 = 24 when 𝑥 = 16 Tell if the following tables represent a direct variation relationship. If they do, find the constant of variation and write the equation that expresses the variation. 4. 6. Graph #4 and #5 on the coordinate plane. What point does each line have in common? This is not by accident. The graph of any direct variation 𝑥 𝑦 3 1 6 2 9 3 5. 𝑥 𝑦 5 10 -­‐1 -­‐2 -­‐4 -­‐8 equation is a LINE that will pass through the ORIGIN 0, 0 . Find the constant of variation, write the equation, then use the equation to find the missing value. 7. If 𝑦 varies directly with 𝑥 and 𝑦 = 198 when 𝑥 = 22, find 𝒚 when 𝑥 = 14. 8. If 𝑦 varies directly with 𝑥 and 𝑦 = 80 when 𝑥 = 32, find 𝒙 when 𝑦 = 100. 9. The distance driven, 𝑑 , varies directly with the time traveled, 𝑡 . If you have driven 175 miles for 5 hours, how long would you drive before you drive 210 miles? 10. At a given time, the length in feet, 𝐿 , of the shadow of an object varies directly as the height of the object, 𝐻 . If the shadow is 27 feet when the height of the object is 12 feet, what is the height of the object if the shadow is 18 feet? 11. If 𝑦 varies directly with 𝑥 and 𝑦 = 16 when 𝑥 = 4, find 𝒚 when 𝑥 = 6. 12. The graph of a direct variation equation is a that passes through the . (see problems 4-­‐6)