Intro to slope-intercept form
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- [Sal] Let's do some practice examples from our intro to slope y intercept exercise. What is the slope of y is equal to negative four x minus three? So you might already recognize, this is in slope intercept form. Just as a reminder, slope intercept form is y is equal to mx plus b, where the coefficient on this x term right over here, that is our slope, and then this constant right over here, that is going to give you your y intercept. So if they're saying, what is the slope here? Well I just need to figure out, what is the coefficient on this x term? And you can see that the coefficient here is a negative four. So that is going to be our m, that is going to be our slope. Now just as a reminder, you have to make sure that it's solved in this way, that is is solved for y, y is equal to something times x minus three, so that's our slope. Let's do another one of these. So we're asked, what is the y intercept of y is equal to negative three x minus two? So once again we already have it in slope intercept form. It's already been solved for y. It's of the form y is equal to mx plus b, where m, our slope, is given right over here, negative three. But they're not asking for our slope, they're asking for the y intercept. Well the y intercept is given by b here, so b is negative two. Pay close attention to the sign here. So b is equal to negative two. But when I look at these choices, I don't see a b is equal to negative two, so what are they talking about? Well a y intercept is, what is the y value when x is equal to zero? And you could see that here, if x was equal to zero then that term goes away and y is equal to b. So if you want to know the point where the graph described by this equation intercepts the y axis, well it's going to be what is y when x is equal to zero? Well when x is equal to zero, y is equal to negative two. And you could see that in our original equation, again. If x were zero, this term would go away, and y would be equal to negative two. So zero, comma, negative two. So it would be that choice right over there. On Khan Academy obviously you just have to click on that, you don't have to shade it in. Let's do one more. Complete the equation of the line whose slope is five, and y intercept is zero, comma, four. So once again the general form is y is equal to our slope times x, if I want to put it in slope intercept form, plus our y intercept. Well they're telling us, our slope is five. Whose slope is five. So we know that m is going to be five. And they tell us that the y intercept is zero, four. So the y intercept, b, that is the value of y when x is equal to zero. So the value of y when x equals zero is this four right over here. So that is going to be four. So I could say y is equal to five times x plus four. And when you're actually entering it on Khan Academy, you would just type it in, or if you're using the app you would use it with your finger. And I always make the mistake of writing y equals, and I type in y equals five x plus four. Notice they already gave you the y equals right over there. That's all you have to do, recognize the slope, the y intercept, and then remember what the slope intercept form actually is.