2.5 Model Direct Variation Direct Variation The equation y = ax represents direct variation between x and y, and y is said to vary directly with x. The nonzero constant a is called the constant of variation. The graph of a direct variation equation y = ax is a line with slope a and y-intercept 0. Graphs have to go through the origin

2.5 Model Direct Variation Example 1: Write and graph a direct variation equation that has (-4, 8) as a solution.

2.5 Model Direct Variation Example 2: Write and graph a direct variation equation that has (3, -9) as a solution.

2.5 Model Direct Variation Example 3: Write and graph a direct variation equation that has (5, 3) as a solution.

2.5 Model Direct Variation Example 4: Hailstones form when strong updrafts support ice particles high in clouds, where water droplets freeze onto the particles. The diagram shows a hailstone at two different times during its formation. a.Write an equation that gives the hailstones diameter d (in inches) after t minutes if you assume the diameter varies directly with the time the hailstone takes to form. b.Using your equation from part (a), predict the diameter of the hailstone after 20 minutes.

2.5 Model Direct Variation Ratios and Direct Variation Because the direct variation equation y = ax can be written as y/x = a, a set of data pairs (x, y) shows direct variation if the ratio of y to x is constant.

2.5 Model Direct Variation Example 5: Great white sharks have triangular teeth. The table gives the length of a side of a tooth and the body length for each of the six great white sharks. Tell whether tooth length and body length show direct variation. If so write an equation that relates them.