Modeling with linear equations: snow

on Monday morning there were 12 inches of snow on the ground the weather warmed up and by Tuesday morning two inches had melted all right so we'll have ten left two more inches melted by Wednesday morning this pattern continued throughout the week until no more snow was left so they're essentially saying that we had 12 inches of snow on the ground on Monday and that every day after that two inches melted so after after Tuesday you would have 10 inches and after Wednesday you'd have eight inches and that pattern continued and what they say is create an equation and a graph to show the relationship between the day and the amount of snow on the ground so let's define a variable that tells us how far away we are from Monday so let's let's let let's let X equal two days after Monday days after Monday days after Monday and then let Y let Y be equal two inches of snow on the ground inches of snow snow on the ground so one way to think about it is okay Y when we have when X is zero when we're on Monday when we're zero days after Monday we're going to have 12 inches of snow on the ground and then every day after that we're going to lose two inches so if we're on Tuesday we're going to have two inches times one because Tuesday is one day so if X is one that means we're on Tuesday if X is two that means we've lost what that means we're two times two we've lost four inches which is what the case is on Wednesday so this is our equation for the relationship between the day and the amount of snow on the ground X is the day how many days after Wednesday I'm sorry after Monday and then why is the inches of snow left on the ground we start with twelve and then every day we lose exactly two inches now let's graph this let's graph it so if this I'll make my vertical axis the y-axis that's inches on the ground Y is equal to in is left on the ground and then the horizontal axis that is our x-axis let me scroll down a little bit this is this is days after days after Monday days after Monday and so we have zero days after Monday we have one two three four five and six and then on Monday which is exactly zero days after Monday that is Monday we have 12 inches on the ground so I'll do it up here so we have 12 we have 12 inches on the ground right there and actually I could do a table if you like let me draw this so if we do X's and X & Y if you do X & Y this is the days after Monday so we want 0 1 2 3 4 5 6 and then on the first day we have 12 inches on Monday zero days after Monday then we lose two inches each day on day one we have 10 day 2 8 6 4 to 0 so let's plot these points we ready plotted 0 12 in that blue color now let's plot 110 110 is right about there it'll be right over there then we can plot 2 8 so off to days after Monday we have 8 inches left on the ground so this is on Wednesday so that's 8 inches and then on on for days or no around 3 days after Monday we have 6 inches on the ground so three days we have 6 inches on the ground and you can see that a line is forming here and then if we go to four days after Monday we have four inches on the ground four days after Monday we have four inches on the ground so that is four and then five days after Monday we have two inches on the ground so five days after Monday we have two inches on the ground and then finally on the sixth day six days after Monday so what do we add Sunday now we are going to have no inches on the ground so that's that right there and you can see that there's this line that formed because this is a linear relationship it looks a little curvy because I didn't draw it perfectly but that is a line so we've done everything we've created the equation we start with twelve inches every day after that we lose two inches and we show it a graph that depicts the relationship