Exercise 19 Page 160

Let's begin by recalling the definition of a proportional relationship.

In this equation m is the constant of proportionality. We are asked to consider the distance equation. d=rt In this equation d is the distance (in feet), r is the rate (in feet per second), and t is the time (in seconds). Since we know that we run for 50 seconds, we can substitute 50 for t into the above formula. d=r( 50) ⇒ d=50r We can see that now our formula represents a proportional relationship because one quantity — distance — is equal to the other quantity — rate — multiplied by a constant value.

Graph

Since we want to use a graph to justify our answer, let's make a table of values for our distance formula.

Let's plot the ordered pairs and draw a line through the points. Our line will be only in the first quadrant of the coordinate plane because negative values of rate do not make sense.

We obtain a line with a slope of 50 that passes through the origin. Therefore, our equation is a proportional relationship.