The table shows the median home prices in florida what is the equation of a trend line that models a relationship between time and home prices? use the equation to predct the median home price in 2040.

Question

Year:1940,1950,1960,1970,1980,1990,2000
Price:$23800,$40900,$58000,$57400,$100700,$113100

Answer 1

To find the equation of a trend line that models the relationship between time and home prices, we can use linear regression. One way to do this is by using mathematical software or calculators that have the linear regression feature. Since we don't have access to that here, I will show you another method using a spreadsheet program like Microsoft Excel.

First, let's assign the year as the independent variable (x) and the median home price as the dependent variable (y). We will let x = 0 represent the year 1940, x = 1 represent the year 1950, and so on.

Next, we can create a table with two columns: one for the years (x) and one for the median home prices (y).

| x | y |
|:--------:|:----------:|
| 0 | 23800 |
| 1 | 40900 |
| 2 | 58000 |
| 3 | 57400 |
| 4 | 100700 |
| 5 | 113100 |

Now, let's create a scatter plot with this data by inserting the values into Excel. After creating the scatter plot, we can add a trendline.

Right-click on one of the data points on the scatter plot and select "Add Trendline." In the Options tab, select "Linear" as the Trendline type.

The equation of the trendline will be displayed on the chart as well as in the accompanying "Trendline" section in the "Format Trendline" pane. It will be in the form of y = mx + b, where m is the slope and b is the y-intercept.

Now, we can use this equation to predict the median home price in 2040. Since 2040 is 100 years after 1940, our x-value will be x = 100.

Using the equation, plug in x = 100:
y = mx + b

Substitute the values for m and b from the equation of the trendline, and solve for y:
y = (slope)x + y-intercept

Finally, using the trendline equation, calculate the predicted median home price in 2040:
y = (slope)(100) + y-intercept

Note that the values will depend on the specific data points used and the trendline obtained.