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

# Slope from equation

CCSS.Math:

## Video transcript

we've got the equation y plus 2 is equal to negative 2 times X minus 3 and what I want to do is figure out what is the slope of the line that this equation describes and there's a couple of ways that you can approach it what my brain wants to do is well I know a few forms where it's easy to pick out the slope for example if I can manipulate that equation to get be in the form Y is equal to MX plus B well then I know that this M here the coefficient on the x-term well that's going to be my slope and B is going to be my y-intercept we cover that in many other videos another option is to get into point-slope form so the general framework or the general the general template for point-slope form is if I have an equation of the form Y minus y1 is equal to M times X minus x1 well then I immediately know that the line that this equation describes is going to have a slope of M once again and here the y-intercept doesn't jump out at you let me make sure you can read this over here the y-intercept doesn't jump out at you but you know a point that is on this line in particular you know you know that the point x1 y1 is going to be on this line x1 comma y1 so let's look at our original example so it might immediately jump out at you that this is actually in point-slope form you might say well ok I see I have a minus x1 so x1 would be 3 I have my slope here and that answers our question our slope would be negative 2 but here it says plus 2 I have to subtract the y1 well you could just rewrite this so it says so you have Y minus negative 2 is equal to negative 2 times X minus 3 and then you see it's exactly this point-slope form right over here so our slope right over there is negative 2 and then if I were to ask you well give me a point that sits on this line you could say all right and x1 would be 3 and a y1 would be negative 2 this point sits on the line it's not the y-intercept but they point on the line and we know the slope is negative two now another way to approach this is to just manipulate it so that we get into slope-intercept form so let's do that let's manipulate it so we get into slope-intercept form so the first thing I brain wants to do is distribute this negative two if I do that I get y plus two is equal to negative 2x negative 2 times negative 3 plus 6 and then I can I can subtract 2 from both sides and then I get Y is equal to negative 2x plus 4 and so here I am in slope y-intercept form and once again I could say all right my am here the coefficient on the x-term is my slope so my slope is negative 2 let's do another example so here this equation doesn't immediately go into either one of these forms so let's manipulate it and if it's in either one of them I like to get into slope y-intercept form it's a little bit easier for my brain to understand so let's do that so let us collect well let's let's get the X's let's just isolate the Y on the right hand sides as to what the 2 is already there so let's add 3 to both sides I'm just trying to get rid of this negative 3 so if we add 3 to both sides on the left hand side we have negative 4 X plus 10 is equal to 2y these cancel out that was the whole point and now to solve for y we have to divide both sides by 2 so if we divide everything by 2 we get negative 2x plus 5 is equal to Y so this is in slope intercept form I just have to lie on the right-hand side instead of the left hand side we have y is equal to MX plus B and so our M is the coefficient on the X term right over here so our slope is once again is negative 2 and here our y-intercept is 5 in case we wanted to know it let's do one more example one more example alright so once again this is in neither slope intercept or point-slope form to begin with so let's just try to get it to slope-intercept form and and like always pause the video and see if you can figure it out yourself alright so let's get all the Y's on the left-hand side isolated and I'll and the X's on the right-hand side so let me get rid of this negative 3x so I'm going to add 3x to both sides now let's get rid of this 3y right over here so let's subtract 3y from both sides you could view this I'm doing two steps at once but once again I'm trying to get rid of this 3x so I'm trying to rid of this negative 3x so I add 3x to the left but I have to do to the right if I want to maintain the equality and if I want to get rid of this 3y well I subtract 3y from here but I have to do it on the left hand side I want to maintain the equality so what do I get that cancels out 5y minus 3y is 2 y is equal to 2x plus 3x is 5x and then these two characters cancel out and so if I want to solve for y I just divide both sides by 2 and I get Y is equal to 5 halves X and I'm done and you might say wait it doesn't look exactly like slope-intercept form where's where's my B well your B if you wanted to see it you could just write plus 0 B is implicitly 0 right over here so your slope your slope is going to be the coefficient on the x-term it's going to be 5 halves and if you want to know your y-intercept well it's it's 0 when x is 0 y 0