I do not understand the answers I was given to this question. 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?

Question

I do not understand the answers I was given to this question. 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?

anonymous · Answer

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.