Answer:
a. Constant of proportionality, k = 1/45
b. hours/miles
c. t = d/45
Explanation:
From the table given, we see that time (hours) increases as distance (miles) increases. We say that time, t varies directly as distance, d
And it is written mathematically as
t α d
t = kd..... (1)
to use the constant of proportionality, k to write a unit rate for the data in the table.
From equation (1), we make k subject of formula
k = t/d
t is in hours and d is in miles, so we can write that
k = hours/miles.
hours/miles is the unit rate for the data
when t = 2, d = 90.
We substitute these values for t = 2, d = 90 into the equation labelled (1)
t = kd
2 = k90
We divide both sides of the equation by the coefficient of k
2/90 = 90k/90
k = 1/45
k = 1/45 is the constant of proportionality.
We then substitute this value of k = 1/45 into equation (1)
t = kd
t = d/45
t = d/45 is the equation to represent the relationship between time t and distance d