Slope from an Equation Simplifying Math

hello this is mr. Buffington and today we are looking at the slope-intercept form of a line what to expect is that we are going to look at a line equation in this form and practice practice practice to learn what the parts are first off let's look at an equation this might look like a line and it is but every line has an equation that's connected to it and tells you what it is mathematically so an equation like this is connected to that line now I want to show you some parts in this equation that translate really easily to this line first of all we can see that the slope of this line is 2 over 1 or 2 it rises 2 and goes over 1 alright there's a lesson on slope if you want to see that but this is the slope of a line is 2 and the great thing is is that that number to 2 over 1 or 2 is right there so this form of a line y equals something times X plus 1 the number in front of X that's the slope so you don't have to know how to calculate slope you just have to know how to look at this equation and pick the number that's in front of the X the other piece of information that we see is the 1 and the 1 is where it crosses the y axis that's called the y-intercept so it crosses the y axis at the point 1 0 1 which is right there and so we can see the slope and the y-intercept that's why this form of a line is called the slope-intercept form of a line so again it's arranged like this Y by itself on the left some number times X plus another number the number that's in front of X is our slope and the number at the end is our y-intercept now let's get rid of all those extra letters and actually do some practical questions with this if I've been given this equation y equals negative 3x plus 2 and they tell me they don't give me a graph they don't show me the line they just say what's the slope all I have to do is point right there whatever number is in front of X is the slope negative 3 that's my slope next question where does this line cross the y-axis that's this 2 it crosses the y axis at the point 0 2 so that is my y intercept and that is my slope every single time the number in front of X is your slope the number by itself off to the side here is your y-intercept if you have the equation arranged like this Y by itself on the left and something times X plus 2 or plus another number that's the information you've got all right your turn I'm giving you a bit of a harder one but I want you to tell me what is the slope follow exactly the same rules that I just showed you put your mouse over where the slope is boom did you put it right there 2/3 that's my slope were you able to get that that's where slope is located whatever the number in front of X it doesn't matter if it's a fraction a decimal positive number they usually won't write it as a decimal but it could be a positive negative doesn't matter that's the slope the number in front of X next question what's my y intercept where does this line cross the y axis put your mouse over the answer boom did you get it negative 7 my y-intercept is negative 7 it crosses the y axis at the point negative 7 or 0 negative 7 all right try again I want you to try this one out what is the slope of this line that's going to be a little bit more challenging what's the slope of this line put your mouse over it boom you said that's not more challenging it's the same thing it's whatever number is in front of X if it's a negative 4 over 5 it's a negative 4 over 5 slope that's it all right last question I want you to pause and solve it where is the y-intercept of this equation where does it cross the y-axis okay welcome back is it did you get 2000 that's exactly it the slope of this line is seven the y-intercept is mm that's right whenever you have a line written in this form with Y by itself on the left some number times X plus another number the number in front of X is the slope the number here is where it crosses the y-axis that is it this is called the slope-intercept form of a line make sure to practice practice practice I hope that lesson was helpful for you you can check out some other videos have a wonderful day

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