The value of an automobile was $15,780 in 1994 and depreciated to $5400 in 1999. Let y be the
value of the automobile in the year x, where x = 0 represents 1994. Write a linear equation in
slope-intercept form that models the value y of the automobile, x years after 1994.
Would the answer be y = -5,400 x + 15,780?
The y-intercept is correct, but -5400 would not be the slope of the line. Remember that slope represents the rate of change, specifically the change in y divided by the change in x. In this case, y is the value of the automobile and x is the year. If that doesn't help, I can clarify it further.
As Christina pointed out, the y-intercept (value at year 0) is correct. However, the formula does not work for year 5, equivalent to 1999, because the depreciation of 5400 was accumulated over 5 years.
You only need a change in the slope to correct the equation.
Another answer choice was y=-2076x + 15,780. Is this correct? If it is I do not understand how they go -2076. Thank you for your help!
I do not understand how -2076 came about.
Since the value depreciated $5400 in 5 years, I would expect the slope to be -$5400/5 = -$1080 per year.
Does that make sense to you?
Yes, the answer would be y = -5,400x + 15,780.
To write a linear equation in slope-intercept form, we need two pieces of information: the slope (m) and the y-intercept (b).
The slope represents the rate of change of the y-values with respect to the x-values. In this case, since the automobile is depreciating, the value is decreasing over time. The formula for slope is:
m = (change in y) / (change in x)
To find the change in y, we subtract the initial value of the automobile ($15,780) from the final value ($5,400).
change in y = 5,400 - 15,780 = -10,380
To find the change in x, we subtract the initial year (1994) from the final year (1999).
change in x = 1999 - 1994 = 5
Now we can calculate the slope:
m = (change in y) / (change in x) = -10,380 / 5 = -2,076
The y-intercept represents the value of the automobile at the starting year (x = 0, which represents 1994). In this case, the value of the automobile in 1994 is $15,780. Therefore, the y-intercept is 15,780.
Now we can plug the values of the slope (m) and the y-intercept (b) into the slope-intercept form equation, which is y = mx + b.
y = -2,076x + 15,780
However, there seems to be a mistake in the answer you provided. The correct equation should have a slope of -2,076, not -5,400.