If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Main content
Current time:0:00Total duration:4:10
CCSS.Math:

Video transcript

what I'd like to do with this video is a few more examples recognizing the slope and y-intercept given an equation so let's start with something that we might already recognize let's say we have something of the form Y is equal to 5x plus 3 what is the slope and the y-intercept in this example here well we've already talked about that we can have something in slope-intercept form where it has a form Y is equal to the slope which people use the letter M for the slope times X plus the y-intercept which people use the letter B for so if we just look at this M is going to be the coefficient on X right over there so M is equal to 5 that is the slope and B is just going to be this constant term plus 3 so B is equal to 3 so this is your y-intercept so that's pretty straightforward but let's see a few slightly more involved examples let's say if we had form Y is equal to 5 plus 3x what is the slope and the y-intercept in this situation well it might have taken you a second or two to realize how this earlier equation is different than the one I just wrote here it's not 5x it's just five and this isn't three it's 3x so if you want to write it in the same form as we have up there you can just swap the 5 and the 3x doesn't matter what or which one comes first you're just adding the two so you could rewrite it as Y is equal to 3x plus 5 and then it becomes a little bit clearer that our slope is 3 the coefficient on the x-term and our y-intercept is 5 y-intercept let's do another example let's say that we have the equation y is equal to 12 minus x pause this video and see if you can determine the slope and the y-intercept alright so something similar is going on here that we had over here the standard form slope intercept form we're used to seeing the X term before the constant term so we might want to do that over here so we could rewrite this as Y is equal to ooh negative x plus 12 negative x plus 12 and so from this you might immediately recognize okay my constant term when it's in this form that's my B that is my y-intercept so that's my y-intercept right over there but what's my slope well the slope is the coefficient on the x-term but all you see is a negative here what's the coefficient well you could view negative x as the same thing as negative 1x so your slope here is going to be negative one let's do another example let's say that we had the equation y is equal to 5x what's the slope and y-intercept there at first you might say hey this looks nothing like what we have up here this is only I only have one term on the right-hand side of the Equality sign here I have two but you could just view this as 5x plus zero and then it might jump out at you that our y-intercept is zero and our slope is the coefficient on the x-term it is equal to five let's do one more example let's say we had y is equal to negative seven what's the slope and y-intercept there well once again you might say hey this doesn't look like what we had up here how do we figure out the slope or the y-intercept but we could do a similar idea we could say hey this is the same thing as Y is equal to zero times X minus seven and so now it looks just like what we have over here and you might recognize that our y-intercept is negative seven y-intercept is equal to negative seven and our slope is a coefficient on the x-term it is equal to zero and that makes sense for a given change in X you would expect zero change in Y because Y is always negative seven in this situation