Question

HELP !! a sandwich shop purchases a used pizza oven for $875. after 5 years, the oven will have to be discarded and replaced. write a linear equation giving the value V of the equipment during the 5 years it will be in use.

Answer 1

Answer: V = -175t + 875

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Explanation:

I'll use y in place of V for now. Also, I'll use x in place of t.

x = number of years

y = value of the oven

Initially, the oven's value is $875, so x = 0 and y = 875 pair up together. The point (0,875) is on the line.

The point (5, 0) is also on the line to indicate that x = 5 years later is when the value of the oven is y = 0 dollars.

We need to find the equation of the line through (0,875) and (5,0)

First we'll need the slope

m = (y2-y1)/(x2-x1)

m = (0-875)/(5-0)

m = -175

The negative slope means the oven is losing 175 dollars in value each year.

The y intercept is b = 875 as this is the initial value of the oven

Put together, y = mx+b turns into y = -175x+875

If we plugged x = 0 into this equation, we'd get y = 875

Similarly, plugging x = 5 into y = -175x+875 leads to y = 0. This helps check we have the right equation

Lastly, replace x with t and replace y with V to end up with V = -175t + 875 which is our final answer.