Graphing a linear equation: 5x+2y=20

create a graph of the linear equation 5x plus 2y is equal to 20 so the line is essentially the set of all coordinate all X's and Y's that satisfy this relationship right over here to make things simpler we're going to do is set up a table where we're going to put a bunch of X values in and then figure out the corresponding Y value based on this relationship but to make it a little bit simpler I'm going to solve for y here so it becomes easier to solve for y for any given X so we have 5x plus 2y is equal to 20 if we want to solve for y let's just get rid of the 5x on the left hand side so let's subtract 5x from both sides of this equation the left-hand side these guys cancel out so we get 2y is equal to the right hand side you have 20 minus 5x and then you can divide both sides of this equation by 2 so you divide both sides by 2 the left hand side we just have a Y and then the right hand side we could leave it that way that actually would be a pretty straightforward way to leave it but what we could call this 20 divided by 2 is 10 minus 5x over 2 or minus five-halves times X and so now using this let's just come up with a bunch of X values and see what the corresponding Y values they are and then just plot them so let me do this in a new color so let me a slightly different shade of yellow so we have X values and then let's think about what the corresponding Y value is going to be so I'll start well I could start anywhere I'll start at X is equal to 0 just because that tends to keep things pretty simple if X is zero then Y is equal to 10 minus five-halves times 0 which is equal to 5 halves times 0 is just 0 so it's just 10 minus 0 or 10 so that gives us the coordinate that point 0 comma 10 when x is 0 Y is 10 so 0 so X is 0 so it's going to be right here at the middle of the x-axis and you go up 10 for the y coordinate 1 2 3 4 5 6 7 8 9 10 so it's right over here so that's the point zero comma 10 let's do another point let's say that X is 2 I'm going to pick multiples of 2 here just so that I get a nice clean answer here so when X is 2 then Y is equal to 10 minus five-halves times 2 and the 2 in the denominator cancels out with this 2 in the denominator in the numerator so it simplifies to 10 minus 5 or just 5 so that tells us the point x equals 2 y is equal to 5 is on the line so 2 X is equal to 1/2 right over here and then Y is equal to 5 we go up 5 1 2 3 4 5 just like that so that's the point 2 5 and when you're drawing a line you actually just need two points we could if we have a ruler or any kind of straightedge we can just connect these two points and if we do it neatly every every point on that line should satisfy this relationship right here just so we get practice I'll do more points so let me do let's say when X is equal to 4 then Y is equal to 10 minus five-halves times 4 this is equal to 5 halves times 4 this is equal to 10 right because the two divide the denominator by 2 you get 1 divide the numerator by 2 you get 2 or 4 over 2 is the same thing as 2 so it becomes 2 times 5 is 10 10 minus 10 is 0 so the point 4 comma 0 is on our line so X is 1 2 3 4 and then Y is 0 so we don't move up at all so we have 4 4 comma 0 and I could keep going I could try other points you could do them if you like but this is plenty just two of these would have been enough to draw the line so let me just let me just draw it so I'll do it in white so the line will look something like this the line will look something the line will look something like something like that and I could keep going in both directions so there you have it that is the graph of our linear equation let me make the my line a little bit bolder just in case you found that first line hard to read so let me make it a little bit bolder I think you get the general idea you