Chapter 55.5: Direct Variation

Definitions• A function in the form y = kx, where k ≠ 0, is a

direct variation. The constant of variation k is the coefficient of x. The variables y & x are said to vary directly with each other.

• To determine if an equation is a direct variation, solve for y. Does it look like y = kx?

Direct Variation• 5x + 2y = 0

• 3y + 4x = 8

Writing Direct Variations• To include point (4, -3)

• To include point (-3, -6)

Writing Direct Variations• You hear thunder 10 seconds after you see

lightning which means you are 2 miles from the lightning. Given the relationship between when we hear thunder and where the lightning occurs varies directly, write an equation for the relationship between time and distance.

Ratios, Proportions & Direct Variations• We can rewrite a direct variation

y = kx as k = y/x• Use the table to determine whether y varies

directly with x. If it does write an equation.

x y y/x

-3 2.25

1 -.75

4 -3

6 -4.5

x y y/x

2 -1

4 1

6 3

9 4.5

Word Problem• The force you must apply to lift an object varies

directly with the object’s weight. You would need to apply .625 lb. of force to a windlass to lift a 28 lb. weight. How much force would you need to lift 100 lbs?

Assignment• p. 264 – 265• 2-28 evens