And Office machine purchased new for $3600 loses $400 each year assuming the value continues to decrease the same amount each year if F X represents the value of the Office machine after eight years which linear function models that given situation

Answer 1

To find the linear function that models the given situation, we need to determine the equation of the line that represents the value of the office machine over time.

Let's assign "t" as the number of years and "V" as the value of the office machine. We know that the office machine is purchased new for $3600 and loses $400 each year.

After one year: V = $3600 - $400 = $3200
After two years: V = $3200 - $400 = $2800
After three years: V = $2800 - $400 = $2400
And so on, until after eight years: V = $3600 - ($400 * 8) = $3600 - $3200 = $400.

We can observe that the value of the office machine decreases by $400 each year. Therefore, the slope of the linear function representing the value over time is -400.

The initial value of the office machine is $3600, so the y-intercept (where the line crosses the y-axis) is $3600.

Using the slope-intercept form of a linear equation (y = mx + b), where m is the slope and b is the y-intercept, we can write the equation as:

V = -400t + 3600

Finally, substituting "F" for "V" and "X" for "t," the equation becomes:

F = -400X + 3600

Therefore, the linear function that models the given situation is F = -400X + 3600.