Question

Rhea wants to purchase a new home house. The house on main street requires a $10,000 down payment and will be a $900 a month on the loan. the other house she likes on Empire Road who has a $4000 down payment and is $1050 per month. Which house has a greater rate of change and what is it? Which house had a greater initial value and what is it?

Answer 1

Explanation:

First, we'll write the cost equations for each house, using the number of months since the initial purchase as the independent variable X:

For the house on Main Street:

Cost = 900X + 10,000

For the house on Empire Road:

Cost = 1050X + 4000

Next, we'll find the rate of change for each house by finding the slope of the respective cost equation:

The slope of the cost equation for the house on Main Street is 900. This means that for every month that passes, the cost of the house will increase by $900.

The slope of the cost equation for the house on Empire Road is 1050. This means that for every month that passes, the cost of the house will increase by $1050.

Now that we have found the rate of change for each house, we can compare them to determine which house has the greater rate of change:

Since the slope of the cost equation for the house on Empire Road is greater than the slope of the cost equation for the house on Main Street (1050 > 900), the house on Empire Road has a greater rate of change.

Finally, we can compare the initial values of each house by comparing the y-intercepts of the respective cost equations:

The y-intercept of the cost equation for the house on Main Street is 10,000, which means that the initial cost of the house is $10,000.

The y-intercept of the cost equation for the house on Empire Road is 4000, which means that the initial cost of the house is $4,000.

Since the y-intercept of the cost equation for the house on Main Street is greater than the y-intercept of the cost equation for the house on Empire Road (10,000 > 4,000), the house on Main Street has a greater initial value.