Writing a linear equation

You are given the 2012 value of a product and 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 V of product in terms of the year.
(Let t=12 represent 2012).

2012 value
$156
Rate
$4.50 increase per year

V = 156 + 4.5 (t - 12)

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
$235,000 $5500 increase per year

235,000=5,500(12)+b

b=235,000-5,500(12)=169,000
V(t)=5,500(t)+169,000

Well, it looks like this product is really going up in the world! Let's write a linear equation that describes its rise to fame (and dollar value).

First, let's define our variables. We'll let V represent the dollar value of the product and t represent the number of years since 2012.

Given that the 2012 value of the product is $156 and the rate of increase is $4.50 per year, we can write the linear equation as:

V = $156 + ($4.50)(t)

So, every year that passes, the value of the product will increase by $4.50. Who knew there was this much money to be made from a product?

To write a linear equation that gives the dollar value of the product in terms of the year, we can use the slope-intercept form of a linear equation, which is given by:

y = mx + b

Here, y represents the value of the product in dollars at a given year, x represents the year (where t=12 represents 2012), m represents the rate of increase per year, and b represents the initial value of the product.

Given that the 2012 value of the product is $156 and the rate of increase is $4.50 per year, we can substitute these values into the equation to find the equation of the line.

When x = 12 (representing 2012), y = 156 (the initial value).

So we have the equation:

156 = (4.50)(12) + b

Simplifying this equation:

156 = 54 + b

Now, to solve for b, subtract 54 from both sides of the equation:

b = 156 - 54
b = 102

Therefore, the linear equation that gives the dollar value of the product in terms of the year is:

V = 4.50t + 102

where V represents the value of the product in dollars and t represents the year (with t=12 representing 2012).

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