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:13:10

Video transcript

let's do a couple of problems graphing linear equations and there are a bunch of ways to graph linear equations and what we'll do in this video is kind of the most basic way where we'll just plot a bunch of values and then connect the dots and I think you'll see what I'm saying so here I have an equation a linear equation I'll rewrite it just in case that was too small y is equal to 2x plus 7 and I want to graph this linear equation before I even take out the graph paper what I could do is set up a table where I pick a bunch of X values and then I can figure out what Y value would correspond to each of those X values so for example if X is equal to let me start really low if x is equal to minus 2 or negative 2 I should say what is y well you substitute negative 2 up here it would be 2 times negative 2 plus 7 so this is negative 4 plus 7 this is equal to 3 if X is equal to I'm just picking X values at random that might be indicative of I'll probably do 3 or 4 points here so what happens when X is equal to 0 then Y is going to be equal to 2 times 0 plus 7 is going to be equal to 7 what about I'm just I just happen to be going up by 2 you could be going up by water you could be picking numbers at random when X is equal to 2 what is y well 2 it'll be 2 times 2 plus 7 so 4 plus 7 is equal to 11 and I could keep plotting points if I like but we could we should already have enough to graph it and actually to plot any line you actually need two points so but so we already have one more than X so actually let me just do one more just to show you this really is a line so what happens when X is equal to 4 and actually just to not go up by 2 let's do X is equal to 8 just to pick a random number then Y is going to be 2 times 8 plus 7 which is let's see well this might go off of our graph paper but 2 times 8 is 16 plus 7 is equal to 23 now let's graph it so let me do my y-axis right there that is my y-axis and let me do my x-axis so you have a lot of positive values here so I want a lot of space on the positive Y side so that is my x-axis and then I use the points X is equal to negative 2 negative 2 that's negative 1 that's 0 1 2 3 4 5 6 7 8 those are our X values and then we can go up into the y axis I'll do it at a slightly different scale because these numbers get large very quickly so maybe I'll do it in increments of in increments of 2 so this could be 2 4 6 8 10 12 14 16 and I could just keep going up there but let's plot these points so this first coordinate I have is X is equal to negative 2 y is equal to 3 so it's the point so I could write my core it's going to be the point negative 2 3 X is negative 2 y is 3 3 would land right over there so that's our first one negative 2 comma 3 then our next point 0 7 we do it in that color 0 7 x is 0 Y is 7 right there 0 7 then we have this one in green here point 2 comma 11 2 comma 11 would be right about there 2 comma 11 and then have this last point it's actually going to fall off of my graph 8 comma 23 8 comma 23 that's going to be way up here someplace if you can even see what I'm doing this is 8 23 and if we connect the dots you'll see a line form so let me connect these dots it shouldn't be I have a obviously hand-drawn it so it might not be a perfectly straight line but if you had a computer do it it would be a straight line so you could keep picking x values and figuring out the corresponding Y values in the situation Y is a function of our X values and if you kept plotting every point you'll get every line if you picked every possible X and plotted every one you get every point on the line let's do another problem at the airport you can change your money from dollars into euros from dollars into euros the service costs five dollars and for every additional dollar you get 0.7 you get 0.7 euros make a table for this and plot the function on a graph use your graph to determine how many bureaus you would get if you give the office $50 all right so I'll write euros euros is equal to so let's see it's going to be dollars so you're going to have to give your dollars there right off of the bat right off of the bat they're going to take five dollars so dollars minus five so immediately there's the service cost five dollars and then everything that's left over this is your leftover you get point seven euros for every leftover dollar so you get zero point seven for whatever's left over so this is the relationship now we can plot points we could actually answer their question right off the bat if you give them $50 we only have to even look at a graph but we will look at a graph right after this so if you did euros is equal to if you have given $50 it would be zero point seven times 50 minus five you gave them 50 they took five as a service fee so this is just $45 and it would be zero point seven times 45 and I could do that right here 45 times zero point seven seven times five is 35 4 times 7 is 28 plus 3 is 31 and then we have only one number behind the decimal only this seven so it's 31 point five so if you give them $50 you're going to get thirty one point five euros euros not a dollar so we answered their question but let's actually do it graphically so let's do a table let's say and maybe I'll get a calculator out I'll refer to that a little bit so let's say dollars you give them dollars and how many euros do you get and I'll just put a bunch of random numbers you got to give them if you give them five dollars they're just going to take your five dollars for the fee you're gonna get five dollars minus five which is zero times 0.7 so you're gonna get nothing back so there's really no good reason for you to do that then if you give them I don't know ten dollars what's going to happen give them ten dollars 10 minus 5 is 5 times 0.7 is you're going to get $3 or I should say 350 euros 3.5 euros you'll get now what happens if you give them I don't know let's say you gave them 30 dollars actually let me say 25 if you give them 25 dollars 25 minus 5 is 20 20 times 0.7 is 14 14 dollars and I'll do one more value let's say give them $55 and this makes the math easy because then you subtract that 5 out 55 minus 5 is 50 times 0.7 is 35 $35 where is that right yep that's right 50 you'll get 35 euros I should say these are all euros I keep one is a dollar so let's plot this and all of these values are positive so I only have to draw the first quadrant here so all of these values are positive and so the dollars let's say let's go income it's a 5 10 15 20 25 30 35 40 45 50 55 I mean my x-axis a little shorter than I needed to all the way up to 55 and the y-axis I'll go increments of 5 so that's 5 5 10 15 20 25 30 35 well that's a little bit too much of an increment 35 all right now let's plot these points I give them 5 dollars I get 0 your so this right here is euros and this is the dollars the dollars is the independent variable and we figure out the euros from it or the euros I get is dependent on the dollars I get if I give ten dollars I get three fifty euros so three fifty it's hard to read and maybe three fifty be right around there buck of twenty five dollars I get 14 euros 25 14 is right about there obviously I'm hand drawing it so it's not going to be quite exact if I get fifty five dollars I get thirty five euros so 55 35 right there and then if I were to connect the dots I should get something that looks pretty close to a line and if I did it if I was a computer it would it would be exactly it would be exactly a line that looks pretty good and then we could we could eyeball what they asked us to do use your graph to determine how many euros you would get if you give the office $50 this is 50 right here so you go Bam Bam Bam Bam Bam Bam Bam Bam all right I'm at the graph then you go all the way you go although actually I drew that that last point on the graph a little bit incorrectly let me let me let 55 35 is right here let me redraw that point so 35 is right there roughly so 55 35 it's auric right there so let me redraw my line it will look I lost 25 25 14 is like right there so my graph looks something like that that's my best attempt now let's answer the question if we give them $50 right there go up up up up up up up $50 the person is going to get you go all the way to the left hand side that's right about 30 150 we figured out exactly using the formula but you can see you can eyeball it from the graph and figure out any amount of dollars if you give them $20 you're going to go all the way over here and you'll figure out that it should be well $20 should be about 750 so now my my the imprecision in my graph my drawing the graph makes a little bit less exact you're going to say 20 minus 5 is 15 15 times actually it'll be a little over $10 which is right it's right over there right if you put $20 in there 20 minus 5 is 15 15 times 0.7 is $10 50 which is right there so you can look at any point in the graph and figure out how many euros you'll get now let's do this one we will do a little bit of reading a graph the graph I think I said use the graph below the graph below shows a conversion chart for converting between weight in kilograms and weight in pounds use it to convert the following measurements so we have kilograms here and pounds here so they want 4 kilograms into weight into pounds so if we look at this right here 4 kilogram 4 kilograms is right there and we just follow where the graph is so 4 kilograms into pounds it looks like I don't know a little bit under 9 pounds so a little bit less than so almost I'll write almost 9 pounds you can't exactly see it's a little less than 9 pounds right there 4 kilograms now 9 kilograms we go over here 9 kilograms all the way up that looks like almost exactly 20 pounds 20 pounds and then here they say 12 pounds into weight in kilograms and actually kilograms is mass but I won't get particular so 12 pounds go over here pounds 12 pounds in kilograms in kilograms looks like five-and-a-half approximately five and a half and then 17 pounds to kilograms so 17 is right there 17 pounds to kilograms looks right about seven and a half seven and a half kilograms anyway hopefully that these examples made you a little bit more comfortable with graphing equations and reading graphs of equations I'll see in the next video