Heart of algebra
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Graphing linear equations — Basic example
- [Instructor] A line is graphed in the xy-plane as shown. Which of the following equations represents the line? They give us a bunch of equations here and so there is several ways we can tackle it. When we look at this, I could see there's two interesting points here, there's the point when x is, let me just write this and actually I'm gonna write a little lower so we can look at it the same time that I look at the equation choices. So we see that when x is a zero, y is one. So that is the y intercept we could say. And then when we could see when x is six, y is zero. When x is six, y is zero, so a very kind of basic way of approaching this is see well, when x is a zero, y needs to be equal to one. When x is zero we get six y is equal to one, well then y is gonna be equal to one sixth, rule that one out. When x is equal to zero, y needs to be equal to one. If x is zero then six y equals six. Yeah, y is going to be equal to one. Now when y is zero, x needs to be equal to six. So if y is 0, this goes away and x is equal to six. So we're done, this is our choice. Now there's other ways that we could do it. We could write it first in slope intercept form and then convert to this form right over here. So let's do it that way as well. We could say that the equation of this line is gonna be y, if I write it in y equals mx plus b form where m is the slope and b is the y intercept. We already know that b is equal to one. So we already know that's one, and what's the slope? Well slope is our change in y for given change in x and we see when our change in x is positive six, when our change in x is positive six, our change in y is negative one, so our slope is we decrease in y by one when we increase in x by six is negative 1/6. So the equation of the line y is equal to negative 1/6 x, this is the slope plus one. And then we could convert to the forms that we have here, so lets see, we could add 1/6 x to both sides and you're gonna get one over six x plus y is equal to one, and that's not quite what we have here. All the coefficients on x are just one. So we can multiply both sides of this times six, and we would get x plus six y is equal to six. Which is exactly the choice that we picked.