after 3 years the estimated value of the workstation was $4400. if the value v in dollars and te age a of the workstation are related by a linear equation, find an equation that express v in terms of a
Since this is a linear equation, we are looking for an equation that can be expressed in the form y=mx + b. Instead of y and x, we are going to use v and a. The equation will be v = ma + b, we have to find the values of m and b.
We will use the coordinate system (a,v) instead of (x,y).
We have two points: (0,8000) which means the system was worth $8000 after 0 years and (3, 4400) which means the system was worth $4400 after 3 years
Slope formula states: m = (y2 - y1)/(x2 - x1), since we are using (a,v) instead of (x,y) our formula is
m = (v2 - v1)/(a2 - a1)
After substituting in our values, we have
m = (4400 - 8000)/(3 - 0)
m = - 3600/3
m = -1200
Now that we have our slope, we can substitute it into the point-slope formula to find our equation. Point slope formual says y - y1 = m(x - x1). Our variation states v - v1 = m(a - a1).
After substituting a point (I chose (0,8000)), we get v - 8000 = -1200(a -0)
Simplifying, we get v - 8000 = -1200a
Add 8000 to each side to get the solution:
v = -1200a + 8000