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Slopes & Intercepts

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alright everybody I'm excited to talk to you today about slopes and intercepts slopes and intercepts in regards to linear relationship so when you get a linear relationship the slope of a line is a ratio and it's the ratio of vertical change to horizontal change we knew or it's rise over run or it's up down change over the Left Right change or we even had it has the change in y over the change in Acts which we fancy formula for but we didn't really care that much about those things except wait a second we saw that formula before but we never really remember what type of what time is there for  will the letter M is used to represent the slope of a line Y who knows why would you what's the letter M represent slope I haven't the slightest idea maybe whoever invented the letter M for slope just didn't speak English or something but whatever the reason is the letter M is used to represent the slope of a line and so you might as well just memorize it okay so what else do we know about the slope of a line is really the same thing as a rate of change and it's the same thing as a unit rate and it's the same thing as the constant of proportionality linear relationship as well so you could say that m is the slope which is also the rate for a problem which is also the Kate constant of proportionality okay now I want to talk to you about intercepts specifically something called y-intercept is just a fancy name for the place where a line intersects or crosses the y-axis so if you have this blue line the Y intercept of this line is 1  the reason is because the place were at Cross the y-axis is right here  and so that crosses the y-axis at 1 some reason we use the letter B to represent the lines Y intercept so for this particular problem b equals one you might want to get down that a y intercept is the B value of a line and the B value are the whiners up is crosses the y-axis here's a few more examples for this upper left graph the y-intercept happens to be three or we could say b equals for this lower left one the y-intercept is negative one or we can say b equals negative one for this one up here the y-intercept is hero cuz it crosses through the zero on the y-axis and then for this one over here there is no wine or set because it's never going to cross y-axis if you need to pause this slide and really look carefully at those graphs and try to find the three and the negative one and the zero you might want to do that just to make sure you understand how to find a y-intercept  now what I want to talk to you about is a bill this is better he's got three got real cards and he's going to earn one more additional got real card per trimester for the rest of the school year let's make a graph a little graph alright he's got 3 got real cards and then after one trimester he's going to have a fourth and then after another trimester is going to have a fit and he could keep on going up and up and up hopefully you see that this is a linear relationship like all the other linear relation set we have been talking about what I want you to now see is where is the Y intercept of this linear relationship it's at 3  because the Y intercept of a line it's like you're starting point in linear relationship Biddle started three got real cards and then he's getting additional ones after that so the fancy word for your starting point in math is called an initial value the initial value of a linear relationship is three then every relationship has to start somewhere right so this linear relationship is starting with an initial value of 3 and then initial value of 3 is just like the B value or the Y intercept of this linear relationship amazing wow some crazy I've never seen anything like it okay what about the slope of this linear relationship the slope of this line it goes up on lower one up on over the slope is one because he's earning one additional card per trimester that's the rate and it's the slope the m equals one and the b equals three so we can take any linear relationship and we can find an M value canopy value by finding the slope which is the rate and by finding the Y intercept witches initial value  now it's your turn  check out this line and tell me what are the slope and the y-intercept and then check out this line and tell me what are its slope and y-intercept and then finally Johnny has $117 in the bank he deposits for additional dollars every week this linear relationship what would the slope be and what would the Y intercept be what would the MB and what would the be be alright that's it slopes and intercepts see you

Uploaded by Jeff Marbut.

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