could you please help me answer this

Question

an average math text book cost $25 in 1980 and $60 in 1995. write an equation that will give the price of a mathbook in any given year , and use this equation to predict the price of the book in 2010.

Answer 1

This is a classic linear equation problem. First, so we can use smaller numbers, let's use "0" for 1980 and add one term for each subsequent year.

 

1980 = 0

1981 = 1

.

.

1995 = 15

.

.

2010 = 30

 

Now that we've established our years (independent quantity), let's take a look at the ordered pairs.

 

At year 0, the cost of the book was $25. We can use the ordered pair (0, 25) to model that.

At year 15, the cost of the book was $60. We can use the ordered pair (15, 60) for this one.

 

Next, let's find the slope, which in this case represents the average yearly increase in price/book.

 

m = (60-25)/(15-0)

m = 35/15 or 7/3

 

So, now that we know the slope, let's create the linear equation that models the situation. We already have the y-intercept (cost at year zero), so let's put it into slope-intercept (y = mx+b) form.

 

y = 7/3x + 25

 

Finally, we can substitute the year for 2010 (30) in for x and get our output value for cost.

 

y = 7/3(30) + 25

y = 95

 

We can expect the book to cost $95 in the year 2010.