Question

I do not understand the answers I was given to this question. Please help!!! The average cost of tuition and fees at private four-year colleges was $16,200, and in 2005 it was $20,100. Sketch a line that passes through the points (2000, 16200) and (2005, 20100).
My question is - find the slope-intercept form of the line in the sketch. What is the y-intercept and does it have meaning in this situation?

Answer 1

QuantumTorch 6 7 0 medals for this answerer.
Alright, I'll solve it showing the steps, and see if that makes a bit more sense. The slope intercept equation for a line is this:
\[y = mx + b\]

The m is the slope of the line. You find the slope using this:
\[\Delta Y \div \Delta X = Y _{1} - Y _{2} div X _{1} - X _{2}\]

Using your values and substituting them in, you have:
\[(20100 - 16200) \div (2005 - 2000) = (3900) \div (5) = 780.\]

So, the slope is 780.

Then we need to find the y-intercept, which in the equation is represented by the variable b. We have a coordinate in the (x,y) format, so we will use those to solve for b:
\[y = mx + b\]
\[16200 = (780)(2000) + b\]
\[16200-1560000 = b\]
\[b = -1543800\]

Obviously b is kinda a wacky number, but it is the point at which the line reaches the y axis.

Answer 2

x is num of years after 2000
y is cost of tuition
slope of 2 points = (y2-y1)/(x2-x1)
slope = (20,100-16,200)/(5-0)
slope = 3900/5 = 78
Every linear line has the form
y=mx+b
m =slope
b=y-intercept
plug in slope and x,y from one point to find b
16,200 = 78*0 + b
16,200 =b

equation of line is
y=78x +16,200

Answer 3

Obviously since you cannot have a negative number for tuition (people never paid you to go to college), the intercept has no meaning.

Answer 4

dumb cow, 3900/5 is not 78, you're off by a zero, and the x coordinate for 16200 is not zero.

Answer 5

oh right thanks, it should be 780
it all depends on your reference point
you can scale the independent value so it make sense to the problem
the initial tuition is 16200 and usually initial x value is 0

Answer 6

its still the same line with the same slope

Answer 7

Yeah but all the x values are waaaay over in the thousands, so it has a long way to get to the y axis.

Answer 8

wait your right, not same line, i just shifted your line over 2000 units
anyway we are prob not helping

Answer 9

Lol well, if he looks at mine it makes sense maybe but he hasn't answered. (or she)

Answer 10

Thanks, all of you. QuantumTorch I believe you are right. That is what I'm using.

Answer 11

using the same equation to estimate tuition and fees in 2001 & compare it to the known value of $17,300. Estimate tuition and fees in 2010.