1. Bellwork Find the slope:
1.) (0, 4) and (3, 5) 4.) What does the equation
2.) (-1, -3) and (4, 8) of a horizontal line look 3.) like?
5.) Of a vertical line?

2. Direct Variation

3. Two variables x and y vary directly if there is a nonzero number k such that the following is true.
y = kx
The number k is the constant of variation. Two quantities that vary directly are said to have direct variation.

4. Find the constant of variation and the slope of each direct variation model.
1.) y = 3x 2.) y = -¼x

5. The graph of any direct variation model will pass through the origin.
The slope of a direct variation model is the constant of variation.

6. Writing a Direct Variation Equation
Write an equation that relates x and y.
Find k.
Plug in k and the new given value to find the new unknown.

7. Example:

8. If you know that y varies directly as x and one set of values, you can use a proportion to find the other set of corresponding values.

9. Example:

10. In 1852, Henri Giffard built the first airship successfully used for transportation. It had a volume of 88,000 cubic feet and could support 5650 pounds. The Graf Zeppelin II, built in 1937 had a volume of 7,063,000 cubic feet, making it one of the largest airships ever built. The weight an airship can support varies directly with its volume. How much weight could the Graf Zeppelin II support?

11. Photo available online at http://www. centennialofflight