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# Parallel lines from equation

## Video transcript

we are asked which of these lines are parallel so parallel lines are lines that have the same slope and there are different lines so they never ever intersect so we need to look for different lines that have the exact same slope and lucky for us all of these lines are in y equals MX plus B or slope-intercept form so you can really just look at these lines and figure out their slopes the slope for line a the slope for line a M is equal to 2 we see it right over there for line B our slope is equal to 3 so these two guys are not parallel and I'll graph it in a second you'll see that and then finally for line C for line C I'll do it in purple the slope is 2 so M is equal to 2 I don't know that purple is too dark for you but so line C and line a have the same slope but they're different lines they have different y-intercepts so they're going to be parallel and to see that let's actually graph all of these characters so line a our y-intercept is negative 6 so the point 0 1 2 3 4 5 6 and our slope is 2 so if we move one in the positive x-direction we go up 2 in the positive y-direction 1 and X up to and why if we go 2 and X we're going to go up 4 and Y we're going to go up 4 in Y and I can just do up to then we're going to go to 4 and you're going to see it's all on the same line so line a is going to look line a is going to look something like do my best to draw it as straight as possible line a I can do a better version than that line a is going to look like well that's about just as good is that what I just drew that is line a now let's do line be a line B the y-intercept is negative 6 0 negative 6 so it does it enter it has the same y-intercept but its slope is 3 so if X goes up by 1 Y will go up by 3 so X goes up by 1 Y goes up by 3 if X goes up by 2 y is going to go up by 6 2 4 six so two and then you go to four six so this line is going to look something like this it's going to look something like this try my best to connect the dots it has a steeper slope and you see that when x increases this blue line increases by more in the Y direction so that is line via notice they do intersect there's definitely not two parallel lines and then finally let's look at line C y-intercept is 5 so 0 1 2 3 4 5 the point 0 5 its y-intercept and it's slope is 2 so you increase by 1 in the X direction you're going to go up by 2 in the Y direction if you decrease by 1 you're going to go down 2 in the Y direction if you increase by well you're going to go to that point you're going to have a bunch of these points and then if I were to graph the line let me do it one more time if I were to decrease by 2 I'm gonna have to go down by 4 right negative 4 over negative 2 is still a slope of 2 so 1 2 3 4 and I can do that one more time get right over there and then you will see the line the line will look like that it will look just like that and notice that line C and line a never intersect they have the exact same they have they have the exact same slope different y-intercepts same slope so they're increasing it the exact same rate but they're never going to intersect each other so line a and line C are parallel