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Slope

Added Oct 28, 2016 •

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okay today's topic is slope what is slope well slope in math is just a weight describe the steepness or the slanting at 7 line so some lines are pretty steep some lines are not super Steep and some some are not steep it all right but when we say that slope is a way to describe the steepness of the slant anus of a line in math we mean in numbers because that's how we do things in math right so what kind of numbers would we use to describe the steepness or slant anus of these lines well first of all the first thing we need to know is sometimes you use positive numbers and sometimes use negative numbers so  this Hello Kitty is driving uphill then that line has a positive slope if Hello Kitty is driving downhill then that line would have a negative slope uphill does it have downhill negative which kind of makes sense right but what if  no yeah there's no slope if you're just going horizontal so that would have a zero for a slope the others would have either a positive number or a negative number now remember when we're deciding whether it's an uphill line or a downhill line slope never goes right to left it always goes left to right just like the way you read that their sentence okay so how about this Maps which one of those graphs has a pause which one has a negative slope and which one has a zero slope okay hopefully you got debt  option C was the one that had a positive slope we can see that that line is going uphill but how do you find the actual value of the slope what's the number does it have a slope of 1 or positive two or positive three well go to look at the actual real-life math definition of the word slope here and there real definition of the word slope is slope is a ratio K so it's something over something and what it's going to compare is vertical change to horizontal change or vertical change over horizontal change in a ratio so remember that the word vertical means up down and the word horizontal means left and right and if you need to positive video and jot that down a little reminder to do that  and then let's take a look at how we would find the vertical change of this line and how we would find the where's Arnold change of this line well we're just going to pick a spot and notice that this line goes up two spots and number one spot and then up two spots and over one so the vertical change is too and the horizontal changes one and therefore the slope of this line is 2 / 1 which reduces tutu so slope is just a number value that tells you that this line goes up to over 1 not Up 3 / 1 not at 5 over one not down to over one but positive to is our slope because you're going up to over 1 Okay so slope is a ratio comparing vertical change to horizontal change so let's take a look at the slope between the point 0, 1 + 1 two  hopefully you see why those coordinates give you those two dots and let's see if we can find slope of the line that goes through those two dots by finding the vertical change and then the horizontal change remember the vertical changes the up-down number so we go up yeah we go up one and then left right how much do we move while we're going to move right one which is kind of like forward one so we're going to go plus one on the vertical side  because we went up 1 and then we're going to go plus one for our Azonto change because we went right one or you could even say forward one and therefore the slope of this line equals 1 1/1 is 1 so remember that slope is a ratio it's a ratio what's the up down number  damn the left right number and since it's a ratio of the up-down number in the left right number like up one or right one sometimes what we do for slope is we say slope is rise over run cuz it's the up-down number over the left right number when is remembering the phrase rise over run is easier than remembering vertical change over horizontal change then you might want to just jot down that slope is sometimes Purdue as a rise over run how about this line well we know that we need to find the vertical change in the horizontal change but where do we start from yeah like the rise or the run from where to where well the good news about this problem as you can just pick any two points on the line like I could pick this point and this point can I count the rise well I have to go from this point to the other one so I'm actually going down 3  and then I'm going to go forward to and so my slope is going to be  -3/2 now you might have counted from one. To the other end on up3 and backwards too and you still would have gotten a slope of negative 3 over 2  and we can talk more about that in class tomorrow but now I want you to try it now I want you to find the slope of this line what's the rise what's the run what's the vertical change what's the horizontal change  okay there's another way to find slope and you can also find slope instead of counting out slope on a if you can use a formula to find the slope and if you use the formula boy look at that formula what does that mean okay well let's break this down you see some wise and some x's there and there's little numbers that go with them and they kind of look like exponents but they're not exponents or Powers cuz they're not up there kind of down what these are talking about is if you have two points each point has coordinates in each coordinate has an x coordinate and y coordinate so  this is talking about the second y-coordinate minus the first y coordinate over the x coordinate minus the first x coordinate so  you could rewrite this formula as second y - first y / second x - four Stacks if that's more helpful than Y2 - y1 over X2 - X1 as long as you understand what it means but where is the second one in the why in the second X in the first X well here they are this is the first x coordinate and the first y-coordinate and this is the second x coordinate and the second y Court so what we're just going to do is a little bit of math where we on the top do the second y minus the first why and then on the bottom we're going to do the second ex- first text so should be 6 minus 2 over negative 1 minus 4 okay and then we just have to do the math what's 6 - 4 + what's -1 - 4 negative 5 so what's our slope -4/5 and we found that slope using of 4 tell me a lot and we never even drew a graph are counted any spots did we okay so what if you wanted to find the slope between these two could we Start Formula and do second y - first why over second x - first X sure we're going to do second y - first why so 2 - over  second x - first X which is 4 - 0  and now we just do the math 2-1 as 1 4 - 0 0 & R hope is one fourth  yeah our slope is 1/4 now what if I decided I don't like that method I don't like you turn the formula can you still please two points 0, 1/4, too and can you find the slope by Counting Silver Run yep up 1/4 hey look you got the same slope either way now maybe drawing awesome counting it out rise over run style is easier but you have to make sure you know how to draw graph and count it out correctly the benefit of doing the formula way is you don't need a graph okay so you can draw a graph of these two points and find the slope or you can use the formula I find the slope between these two points either one is fine or you could do both ways and just use that as a way to double check and see if you got the right answer but either way see if who came up with the slope from 10, 7 to 8, 6 all right to review slope is a ratio it's a ratio what over what  vertical change over horizontal change and you can find slope using that vertical change over horizontal change ratio AKA rise over run or you can find slope using  second y - first White / second x - first X thanks for listening thanks for watching thanks for taking great notes and thanks for doing those practice problems we will talk more about slope tomorrow  see

Uploaded by Jeff Marbut.

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Slope

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