Two farmers use combines to harvest corn from their fields. One farmer has 600 acres of corn, and the other has 1000 acres of corn. Each former's combine can harvest 100 acres per day. Write two equations for the number of acres y of corn not harvested after x days. Are the graphs of the equations parallel, perpendicular, or neither? How do you know?

Question

Two farmers use combines to harvest corn from their fields. One farmer has 600 acres of corn, and the other has 1000 acres of corn. Each former's combine can harvest 100 acres per day. Write two equations for the number of acres y of corn not harvested after x days. Are the graphs of the equations parallel, perpendicular, or neither? How do you know?

Answer 1

y=Initial amount- rate*timeindays.

I bet the graphs are parallel, they have the same slope (rate)

Answer 2

Let's denote the number of acres of corn not harvested after x days for the first farmer as y1 and for the second farmer as y2.

For the first farmer:
- The total number of acres of corn that the first farmer has is 600 acres.
- Each day, the first farmer's combine can harvest 100 acres.
- Therefore, the number of acres of corn not harvested after x days for the first farmer can be represented as y1 = 600 - 100x.

For the second farmer:
- The total number of acres of corn that the second farmer has is 1000 acres.
- Each day, the second farmer's combine can harvest 100 acres.
- Therefore, the number of acres of corn not harvested after x days for the second farmer can be represented as y2 = 1000 - 100x.

Now, let's analyze the equations and determine if their graphs are parallel, perpendicular, or neither.

The given equations for the number of acres of corn not harvested after x days for the two farmers are:

y1 = 600 - 100x (Equation 1)

y2 = 1000 - 100x (Equation 2)

We can see that the slopes of both equations are the same (-100). Since the slopes are the same, the graphs of the equations will be parallel.

Answer 3

To write the equations for the number of acres of corn not harvested after a certain number of days, we can start by defining some variables:

Let's use:
x = the number of days
y1 = the number of acres of corn not harvested by the first farmer
y2 = the number of acres of corn not harvested by the second farmer

Now let's work on deriving the equations:

1) First Farmer's Equation:
The first farmer has 600 acres of corn and can harvest 100 acres per day. This means that after x days, the first farmer would have harvested 100x acres. Therefore, the number of acres of corn not harvested by the first farmer is given by:
y1 = 600 - 100x

2) Second Farmer's Equation:
The second farmer has 1000 acres of corn and can also harvest 100 acres per day. So after x days, the second farmer would have harvested 100x acres. Thus, the number of acres of corn not harvested by the second farmer is:
y2 = 1000 - 100x

Now let's analyze the slopes of the two equations to determine the relationship between their graphs:

The equations of the two lines are in the slope-intercept form y = mx + b, where m represents the slope. The slopes of the two equations are both -100.

Since the slopes are the same (-100), the graphs of the equations are parallel. This is because the rate at which each farmer harvests the corn is the same (100 acres per day) and does not change.

Therefore, the answer is: The graphs of the equations are parallel.

Note: To determine whether two graphs are parallel or perpendicular, we compare the slopes of the equations. If the slopes are the same, the graphs are parallel. If the slopes are negative reciprocals (opposite signs and inverted values), the graphs are perpendicular.