Question

consider the distance equation d=rt, where d is the distance (in feet), r is the rate (in feet per second), and t is the time (in seconds). you run fir 50 seconds. Are the distance you run and the rate you run at proportional? Use a graph to justify your answer.

Answer 1

yes, they are proportional

Explanation:

A proportion is a relation that can be modeled by a straight line through the origin. The equation will have the form ...

y = kx

where x is the independent variable, y is the dependent variable, and k is a constant of proportionality.

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If you start with the equation relating distance, rate, and time:

d = rt

and you fix the time at 50 seconds, then the equation becomes ...

d = 50t

This is the equation of a proportion with a constant of proportionality of 50. It tells you the distance run is proportional to the rate you run. When this equation is graphed, it is a straight line through the origin.