Answer:
Cyclist A 12 mi/h
Cyclist B 5 mi/h
Cyclist C 9 mi/h
Cyclist D 10 mi/h
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]
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
In this problem the relation between the distance and the time represent a direct variation
Let
y -----> the distance in miles
x ----> the time in hours
The unit rate is the same that the slope or constant of proportionality of the linear equation
Cyclist A
we have
The cyclist can ride 24 miles in 2 hours
The unit rate is equal to divide the total distance by the total time
so
[tex]\frac{24}{2}=12\ \frac{mi}{h}[/tex]
Cyclist B
Looking at the table
For x=1 h, y=5 mi
[tex]k=y/x[/tex]
substitute
[tex]k=\frac{5}{1}=5\ \frac{mi}{h}[/tex]
Cyclist C
we have
[tex]y=9x[/tex]
Remember that the unit rate is equal to the slope
so
[tex]m=9\ \frac{mi}{h}[/tex]
Cyclist D
Looking at the graph
For x=1 h, y=10 mi
[tex]k=y/x[/tex]
substitute
[tex]k=\frac{10}{1}=10\ \frac{mi}{h}[/tex]
