Question

the distance d you bike varies directly with the amount of time t you bike. suppose you bike 9.8 mi in 1.25 h. what is an equation that relates d and t? what is the graph of the equation?

write an equation that relates d and t. choose the correct answer below

a. ( d = 1.25t )

b. ( d = 9.8t )

c. ( d = 12.25t )

d. ( d = 7.84t )

Explanation:

Step1: Recall direct variation formula

For direct variation, the formula is \( d = kt \), where \( k \) is the constant of variation (speed in this case).

Step2: Calculate the constant \( k \)

We know \( d = 9.8 \) mi and \( t = 1.25 \) h. Using \( k=\frac{d}{t} \), we substitute the values: \( k = \frac{9.8}{1.25} \). Calculating this, \( \frac{9.8}{1.25}=7.84 \).

Step3: Write the equation

Substitute \( k = 7.84 \) into the direct variation formula \( d = kt \), we get \( d = 7.84t \).

Answer:

D. \( d = 7.84t \)