Answer:
Part A) Is a directly proportional
Part B) The constant of proportionality is
Part C) The equation is
Part D) acres of soybeans
Step-by-step explanation:
Part A) Are the number of acres of corn and the number of acres of soybeans directly proportional or inversely proportional?
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form
Let
x-----> the number of acres of corn
y----> the number of acres of soybeans
so
if the number of acres of corn increases then the number of acres of soybeans increases
if the number of acres of corn decreases then the number of acres of soybeans decreases
therefore
The relationship is a directly proportional
Part B) What is the constant of proportionality?
we have that
For x=200, y=50
substitute
Part C) Let x equal the number of acres of corn and y equal the number of acres of soybeans. Write an equation to show this relationship.
The linear equation that represent the direct variation is equal to
we have
substitute
Part D) How many acres of soybeans can the farmer plant this year if he plants 250 acres of corn?
For x=250
Find the value of y
substitute in the linear equation the value of x and solve for y
-----> acres of soybeans