Problem 6 help needed Algebra

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 to $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)

A)Find the slope of the line between these 2 points show your work.

B)Interpret the slope of the line in the context of the problem, use a complete sentence.

C)Write an equation of a linear model in the form y = mx+b to describe the data, show your work.

D)Interpret the meaning of the Y intercept in the context of the problem.

E)Use your equation to predict the cost of tuition at this Oregon community college in 2023.

Answer 1

Hi Angeles L

The slope, m, 97 shows the rate of increase, 97 dollars per year over the 12 years between your given points

y= 97x + 2765

In 2000 (your starting point) the tuition was 2765 this is also the y intercept over the time frame given in your data

In 2023 tuition will be $4996

First you should assign your points (x₁, y₁) and (x₂, y₂)

To find the slope between the given two points you use the formula for the slope

m = (y₂ - y₁)/(x₂ - x₁)

m = (4414 - 3250)/(17 - 5) = 97

If m is positive the it will slant upward to show the increasing tuition

You can start with form y = mx + b by plugging in the slope calculated above

y = 97x + b

Use one of your points to solve for b

4414 = 97(17) + b

4414 = 1649 + b

4414 - 1649 = b

2765 = b

y = 97x + 2765

For your plot per the information given x represents the time since 2000 while the points given represent the change from 2005 to 2017 and finally you will want to include enough on your x and y axis to predict the cost in the year 2023. You could let the year 2000 be your starting point or year zero and number from 0 to 25. You can graph your y = mx +b at Desmos.com, use a graphing calculator or do it by hand. Make sure you label your axis correctly where x would be the number of years since 2000 and y would be the cost in dollars.

Do Graph your line to confirm the presence of the two points given.

Give it a try.