For tax purposes, you may have to report the value of your assets, such as cars or refrigerators. The value you report drops with time. "Straight-line depreciation" assumes that the value is a linear function of time. If a $1020 refrigerator depreciates completely in seven years, find a formula for its value as a function of time. (Let x represent the time in years and y be in terms of dollars.)
I thought that the answer would be y= -145.7142857x + 1020 but I was told that it was wrong. I thought "b" in y=mx+b would be 1020 because that is how much the item is worth brand new. And I got the large negative slope value by using the points (0,1020) and (7,0) that I derived from the problem.
How do I go about solving this?
I believe you are correct.
Thank you!
To solve for the formula of the value as a function of time, you're on the right track by using the equation y = mx + b, where m represents the slope and b represents the y-intercept.
Given that the refrigerator is worth $1020 brand new and depreciates completely in seven years, we can use the points (0, 1020) and (7, 0) to find the equation.
To find the slope (m), we use the formula m = (y2 - y1) / (x2 - x1) with the points (0, 1020) and (7, 0).
m = (0 - 1020) / (7 - 0)
m = -1020 / 7
m ≈ -145.714
So, your slope is correct.
Now, let's find the y-intercept (b) by substituting the values of a known point (0, 1020) into the equation (y = mx + b).
1020 = -145.714 * 0 + b
1020 = b
Therefore, your equation should be y = -145.714x + 1020.
Your answer was correct, and it seems there might have been a misunderstanding or mistake in the explanation you received. Double-check your solution and feel confident in your equation.