cost of tuition algebra help word problem

Question

The average cost of tuition at a public community college in Oregon was $3,520 in 2005 and this cost has increased somewhat linearly at $4,414 in 2017. Let x be the number of years since 2000 and let y be the cost of tuition. The given information can be written as two data points (x,y). (5,3520) and (17,4414)

-Find the slope of the line between these two points, show your work

-Interpret the slope of the line in the context of the problem using a complete sentence.

-write an equation of a linear model in form y=mx+b to describe the data, show your work

-interpret the meaning of the y intercept in the context of this problem

-Use your equation to predict the cost of tuition at this oregon community college in 2023.

Answer 1

The slope in this case is the rate of change of tuition over time (chg in y/chg in x) when time is graphed on the x-axis and $'s on the y-axis.

m = slope is therefore (4414 - 3520)/(17 - 5) = 894/12 = $74.50/year. (x = the number of years since 2000)

The tuition will increase by $74.50 in each year.

For y = mx + b we have the m, now we need the b (y-intercept).

Use either of the two ordered pairs - I'll use (5, 3520)

3520 = 74.50(5) + b

3520 = 372.50 + b; b = 3520 - 372.50 = $3147.50 is the y-intercept, corresponding to the tuition in year 0 (2000)

y = 74.50x + 3147.50

For 2023, that's 23 years after 2000, so x = 23.

y = 74.50(23) + 3147.50 = 1713.50 + 3147.50 = $4861

Answer 2

Start with two-point form

(y - 3520) / (x - 2005) = (4414 - 3520) / (2017 - 2005)

You convert and answer.