Worked examples: slope-intercept intro | Mathematics I | High School Math | Khan Academy

Do some practice examples from our intro to slope-intercept exercise.

What is the slope of y is equal to negative 4x minus 3?

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, 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 it 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 3.

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 2. Pay close attention to the sign here, so b is equal to negative 2.

But when I look at these choices, I don't see a b is equal to negative 2. So what are they talking about? Well, a y-intercept is what is the y-value when x is equal to 0. And you could see that here. If x was equal to 0, 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 was zero, this term would go away, and y would be equal to negative two.

So zero, comma, negative 2. 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 5 and y-intercept is 0, 4. So once again, the general form is y is equal to our slope times x. If I want to put in slope-intercept form plus our y-intercept, well, they're telling us our slope is 5, whose slope is 5.

So we know that m is going to be 5, and they tell us that the y-intercept is 0, 4. So the y-intercept b, that is the value of y when x is equal to 0. So the value of y when x equals 0 is this 4 right over here. So that is going to be 4.

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. Now, just you have to—they already gave you the y equals right over there. But that's all you have to do: recognize the slope, the y-intercept, and then remember what the slope-intercept form actually is.