Answer:
Part a) 0.20 revolutions per foot of distance traveled
Part b) The slope of the graph is [tex]m=5\frac{ft}{rev} [/tex]
Step-by-step explanation:
step 1
Find the slope
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
Let
x ----> the number of revolutions
y ----> the distance traveled in feet
we have the point (2,10) ----> see the graph
Find the value of the constant of proportionality k
[tex]k=y/x=10/2=5\frac{ft}{rev} [/tex]
Remember that in a direct variation the constant k is equal to the slope m
therefore
The slope m is equal to
[tex]m=5\frac{ft}{rev} [/tex]
The linear equation is
[tex]y=5x[/tex]
step 2
How many revolutions does Charmaine make per foot of distance traveled?
For y=1
substitute in the equation and solve for x
[tex]1=5x[/tex]
[tex]x=1/5=0.20\ rev[/tex]
