Question

(15 POINTS!) The graph shows the distance a ghost crab can run over time the D equals the distance in meters and the t equal the time in seconds which is a direct variation equation for this relationship

A. d= 3/5t
B. d = 5/3t
C. t= 5/3d
D. t= 2/5d

Answer 1

Option B. d = 5/3t

Explanation:

see the attached figure to better understand the problem

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form
`y/x=k` or
`y=kx`

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

Let

d -----> the distance in meters

t ----> the time in seconds

Looking at the graph we have the point (3,5)

That means ----> For t=3 sec, d=5 m

Find the value of k

`k=d/t`

substitute the value of y and the value of x

`k=5/3`

The linear equation is

`d=kt`

substitute the value of k

`d=(5)/(3)t`