In 1980 the average price of a home in Brainerd County was $97,000. By 1986 the average price of a home was $109,000 Write a linear model for the price of a home, P, in Brainerd County as a function of the year, t. Let t=0 correspond to 1980
so treat your data as two ordered pairs
(0,97000) and (6,109000)
Just like in a normal x-y equation,
slope = (109000-97000)/(6-0)
= 12000/6 = 2000
using (0, 97000) , which would be the y-intercept
y = 2000x + 97000
what would be the x intercept
{0,9700} and {6,109000} just like in a normal x-y equation, slope={109000-97000}/{6-0} =12000/6=2000
using {0,97000} ,which would be the y-intercept y=2000x+97000
To write a linear model for the price of a home in Brainerd County, we can use the slope-intercept form of a linear equation, which is:
P = mt + b
Where P is the price of a home, t is the year, m is the slope, and b is the y-intercept.
Given that the price of a home in 1980 was $97,000 and in 1986 was $109,000, we can find the values of m and b.
Let's start by finding the slope, m. The slope is calculated using the formula:
m = (y2 - y1) / (x2 - x1)
Where (x1, y1) is the coordinate for 1980 (0, $97,000), and (x2, y2) is the coordinate for 1986 (6, $109,000).
m = ($109,000 - $97,000) / (6 - 0)
m = $12,000 / 6
m = $2,000
Next, let's find the y-intercept, b. We can use the point-slope form of a linear equation:
y - y1 = m(x - x1)
Substituting the values (0, $97,000) for (x1, y1):
P - $97,000 = $2,000(t - 0)
P - $97,000 = $2,000t
Simplifying, we get:
P = $2,000t + $97,000
So, the linear model for the price of a home, P, in Brainerd County as a function of the year, t, is:
P = $2,000t + $97,000