Question

3) A rabbit and turtle are in a race. Is the relationship between distance traveled and time proportional? Show your work. If so, write an equation that represents the relationship. Turtle's run: distance (meters) time (minutes) 54-1082 34-40517 su Holio 108 2 405 7.5 34 = 1768.5/32.75 540 10 dit -54 1768.5 32.75 id/txt = 544 d- 547 Rabbit's run: distance (meters) time (minutes) 800 1 900 5 1107.5 20 1524 32.5

Answer 1

A proportional relationship is when two quantities vary directly with each other and has the form:

`y=kx`

Rabbits run:

To know if it's proportional, we have to know the constant of the previous equation:

`k=(y_1-y_2)/(x_1-x_2)`

Solving these constants with different values given:

`k=(800-900)/(1-5)=(-100)/(-4)=4`
`a=(800-1524)/(1-32.5)=(-724)/(-31.5)=22.98`

Based on those values we can see that the relationship is not proportional.