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Applying Slope

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alright hello today we are going to be talking about not just slope but applying slope what is slope what does it mean what can we do with sloped so in order to help us understand slope I want to think about feet feet no not like not like your feet and how they might smell or how clean or dirty they might be but feet like the unit of measurement feet so we all know that one foot is equal to 12 inches I think we all know that what I want you to see is that we can make a ratio of that and say that 12in over one foot is kind of like the ratio are the rate when we talk about converting inches to feet or converting feet to inches now we can take this ratio which is a rate and we could make it into a table and I could say if I have one foot I have 12 inch if I have to I have 12 more which is 20 Sanchez if I have 3 at 36 in this is all kind of Elementary level stuff we know how to fill in a table like that what we can do with this as we can also assign the input output relationship is an XY make this into a linear function you can turn it into a graph so we can take this and linear relationship and we can make it into a graph by just plotting those pairs of numbers we can go like this and like this and it's a fairly steep line but it is a line okay what is a linear relationship what would the slope of this line be the slope of this line actually is 12 / 1 because it goes up 12 / 1 up 12 / 1 up 12 / 1 so wait a second what that is the 12 ever one is kind of an amazing number for this particular relationship for this function slope here 12 / 1 is the same as the rate of change its the same as the unit rate and the amazing truth of any linear function any linear function is going to have a slope that's the same as its rate of change and that's what we call a linear relationship because in order for the dots to make a straight line they have to be going up and over up and over in the same ratio in an order for a relationship to be linear the rate of change has to be constant it has to be an unchanging rate of change so what we basically need to know about slope today is the slope is basically the same thing as rate or rate of change now we can make this into it an equation by taking that rate of change and 12 and putting it into the equation and saying in this case y equals 12 x number of inches equals 12 times the number of feet and what you notice there is it in the equation the 12 represents the rate of change and it also represents the slope so that's pretty much all we need to know today I just want you tried this with a little practice problem tell me about the relationship between quarters and dollars in table form and in form if you can do that and me verify the slope compared to the rate or the ratio then I think you will have understood today's lesson that's all we have to say today remember math is everywhere I'll see you tomorrow

Uploaded by Jeff Marbut.

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Applying Slope

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