Question 171447
A recent downturn in economy is causing a man's 401(k) to lose value at a linear rate . On january 1 the account was worth $120,000 and on August 1 it was worth $96,000. If the current trend continues, on december 1 it will be worth how much?
.
worth along y-axis
months along x-axis
.
january 1 the account was worth $120,000 
(1,120000)
August 1 it was worth $96,000
(8,96000)
.
slope
m = (y2-y1)/(x2-x1) 
m = (96000-120000)/(8-1) 
m = (96000-120000)/(8-1) 
m = -24000/7
m = -3428.57 (slope)
.
y = mx + b
96000 = -3428.57(8) + b
96000 = -27428.57 + b
123428.57 = b
.
Our equation of the line is then:
y = -3428.57x + 123428.57
.
where
x is the month (1-12)
y is the worth of portfolio
.
So, to find value for December, set x to 12 and calculate y:
y = -3428.57x + 123428.57
y = -3428.57(12) + 123428.57
y = -41142.84 + 123428.57
y = $82285.73