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CCSS.Math:

deidre is working with a function that contains the following points these are the X values these are y values and they ask us is this function linear or non-linear so linear functions the way to tell them is for any given change in x is the change in y always going to be the same value for example if when x went for any one step change in x is the change in y always going to be 3 is it always going to be 5 if it's always going to be the same value you're dealing with a linear function if for each change in X so over here X is always changing by 1 so since X is always changing by 1 the change in Y's have to always be the same if they're not then we're dealing with a nonlinear function we can actually show that plotting out if the changes in X were going by different values if this went from 1 to 2 and then 2 to 4 what you'd want to do then is divide the change in Y by the change in X and that should always be a constant like let me write that down linear if it's if something is linear then the change in Y change in Y over the change in X over the change in X always constant always constant now in this example the change in X's are always 1 all right we go from 1 to 2 2 to 3 3 to 4 4 to 5 so in this example the change in X is always going to be 1 so in order for this function to be linear our change in Y needs to be constant because we're just going to take that and divide it by 1 so let's see if our change in Y is constant when we go from 11 to 14 we go up by 3 when we go from 14 to 19 we go up by 5 so I already see that it is not constant we didn't go up by 3 this time we went up by 5 and here we go up by 7 and here we're going up by 9 so we're actually going up by increasing amounts so we're definitely dealing with a non linear function and we can see that if we graph it out so let me draw I'll do a rough graph here so let me make that my vertical access my y-axis and we go all the way up to 35 so I'll just do I'll just do 10 20 30 actually I can do it I can do a little bit more granular than that I could do 5 10 15 20 25 30 and then 35 and then our values go one through five so I'll do it on this axis right here they're not obviously at the exact same scale so I'll do one two three four and five and so let's plot these points so the first point is 111 when X is 1 Y is 11 this is our x-axis when X is 1 Y is 11 that's right about there when X is 2 y is 14 when X is 2 y is 14 that's right about there when X is 3 y is 19 when X is 3 y is 19 right about there when X is 4 y is 26 when X is 4 y is 26 right about there and then finally when X is 5 y is 35 when X is 5 y is 35 right up there so you can immediately see that this is not tracing out a line if this was linear if this was a linear function then the all the points would be on a would be on a line that looks something like that that's why it's called a linear function in this case it's not it's nonlinear it's the rate of increase as X changes is going up