Question

Directions: Determine whether each linear function is a direct variation. If so, state the constant of variation. 1. 11 12 13 Hours, x Distance, y (miles) 14 193 154 167 180

Answer 1

the function is not a direct variation.

Step-by-step explanation:

For the function to be a direct variation, it must follow the formula:

y = mx

where m = constant of proportionality.

The constant of proportionality must be the same for each of the points

when x = 11, y = 154

Inserting the above into the formula:

154 = 11m

154/11 = 11m/11

m = 14

when x = 12, y = 167

167 = 12m

m = 167/12 = 13.92

when x = 13, y = 180

180 = 13m

m = 180/13 = 13.85

when x = 14, y = 193

193 = 14m

m = 193/14 = 13.79

Since the constant of proportionality, m is not the same for all the given points, the function is not a direct variation.