Writing a Linear Equation
You are given the 2012 value of a product and the rate at which the value is expected to change during the next 5 years. Use this information to write a linear equation that gives the dollar value V of the product in terms of the year.
(Let t=12 represent 2012).
2012 Value Rate
$ 156 $4.50 increase per year
2012 value
$156
Rate
$4.50 increase per year
To write a linear equation that represents the change in value of the product over time, we need to first determine the initial value and the rate of change.
In this case, the initial value is given as $156 in 2012 (t=12), and the rate of change is $4.50 increase per year.
The general form of a linear equation is:
V = mt + b
where V represents the dollar value of the product, t represents the year, m represents the slope (rate of change), and b represents the y-intercept (initial value).
We can plug in the values we have to derive the equation.
V = 4.50t + 156
Therefore, the linear equation that gives the dollar value V of the product in terms of the year is V = 4.50t + 156.