I need help solving this. I do not get it one bit.

The median home sale price in country A has been rising approximately linearly since 1995. The median home sale price in 1995 was ​$110,500. The median home sale price in 2004 was ​$194,200. Let P be the median home sale price and let t be the number of years since 1995.

Determine a function​ P(t) that fits this data.

To determine a function P(t) that fits the given data, we can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept.

In this case, the slope represents the rate at which the median home sale price is rising per year, and the y-intercept represents the median home sale price in 1995.

Given that the median home sale price in 1995 was ​$110,500, we can substitute this as the y-intercept, meaning b = 110,500.

To find the slope, we can use the formula:

slope (m) = (change in y) / (change in x)

where "change in y" is the difference in median home sale prices, and "change in x" is the difference in years.

The change in median home sale prices from 1995 to 2004 is ​$194,200 - ​$110,500 = ​$83,700.

The change in years is 2004 - 1995 = 9 years.

Now, we can substitute these values into the formula to find the slope:

slope (m) = (83,700) / (9)

Now, we have the slope and y-intercept, so the function P(t) is:

P(t) = mt + b

Plugging in the values, we get:

P(t) = (83,700/9)t + 110,500

Simplifying further:

P(t) = 9300t + 110,500

Therefore, the function P(t) that fits this data is P(t) = 9300t + 110,500.

To determine a linear function P(t) that fits the given data, we can use the slope-intercept form of a linear equation, which is:

y = mx + b

In this case, P(t) represents the dependent variable (the median home sale price), and t represents the independent variable (the number of years since 1995).

First, let's find the slope (m) of the linear equation using the two data points provided. The slope can be calculated using the formula:

m = (y2 - y1) / (x2 - x1)

Using the data points (1995, $110,500) and (2004, $194,200), we have:

m = ($194,200 - $110,500) / (2004 - 1995)

m = ($83,700) / (9)

m = $9,300

Next, we need to determine the y-intercept (b) of the linear equation. We can use the point-slope form of a linear equation to calculate the y-intercept:

y - y1 = m(x - x1)

Using the point (1995, $110,500), we have:

P - $110,500 = $9,300(t - 1995)

Simplifying the equation, we get:

P = $9,300t - $18,498,500 + $110,500

P = $9,300t - $18,388,000

Therefore, the function P(t) that fits the given data is:

P(t) = $9,300t - $18,388,000

A has been rising approximately linearly

means you are looking for a function like
A = mt+b

Since t=0 for 1995, you know that
A = mt + 110,500

The home price rose by 194,200-110,500 = 83700
2004 is 9 years after 1995.
So, the slope of the line is 83700/9 = 9300

The line is thus

A = 9300t + 110500