Lesson 4.6 Model Direct Variation Word Problems Essential Question: How do you write and graph direct variation equations?

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Presentation transcript:

Lesson 4.6 Model Direct Variation Word Problems Essential Question: How do you write and graph direct variation equations?

What is direct variation? A relationship between two variables x and y if there is a non zero number a such that y is said to vary directly with x

Ratios and Direct Variation

Tell whether the table represents direct variation. If so, write the direct variation equation. x12346 y

Tell whether the table represents direct variation. If so, write the direct variation equation. x-3135 y-20246

Tell whether the table represents direct variation. If so, write the direct variation equation. x24816 y1246

Downloading Files The table shows the amount of time t (in seconds) it takes to download a file of size s (in kilobytes). - Explain why s varies directly with t. - Write a direct variation equation that relates s and t. - How long will it take to download an 800-kilobyte file?

Saltwater Aquarium The number s of tablespoons of sea salt needed in a saltwater fish tank varies directly with the number w of gallons of water in the tank. A pet shop owner recommends adding 100 tablespoons of sea salt to a 20 gallon tank. –Write a direct variation equation that relates w and s. –How many tablespoons of salt should be added to a 30 gallon saltwater fish tank?

Meteorology Hailstones form when strong updrafts support ice particles high in clouds, where water droplets freeze onto the particles. The diameter of the hailstone varies directly with the time it takes to form. The diagram shows a hailstone at two different times during its formation. –Write a direct variation equation that relates diameter d and time t. –What is the diameter of the hailstone after 20 minutes?

An object that weighs 100 pounds on Earth would weigh just 6 pounds on Pluto. Assume that the weight P on Pluto varies directly with weight E on Earth. –Write a direct variation equation that relates P and E. –What would a boulder weighing 750 pounds on Earth weigh on Pluto?

How do you write and graph direct variation equations?

Ticket Out the Door If the table shows direct variation, write the equation. x1236 y