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CCSS.Math:

Luis and Kate have two video games they want to play they plan to spend exactly 45 minutes playing the two games they want to use an equation to express the relationship between the number of minutes they spend playing Super Bologna man and the number of minutes they spend playing you have to cut the wire can this relationship be represented using a linear equation so let's see if it can so let's define some variables for let's define one variable for the amount of time the amount the number of minutes so the number of minutes they spend playing Super Bowl on you man let's define that as well let's just say that's X so X is equal to time playing playing Bologna man I'll write Bologna right here below in your mane and let's define y as y is equal to the number of minutes they spend playing you have to cut the wire so it's time time playing I'll just call it the cut the wire I'll just call it wire for short so if we have the minutes they play time playing Bologna and the time playing cut your wire if I were to add those two together so if I say X plus y I'll write the plus in a neutral color X plus y what does this need to be equal to the time I play blown your man plus the time I play have to cut the wire well if I add them together they they want to spend exactly 45 minutes playing both games so this is going to be equal to 45 minutes now we have set up an equation that represents the that relates the time playing Bologna man and the time playing you have to cut or you have to cut the wire but now we have to think about is this a linear relationship so one way to think about it it is the real giveaway for a linear relationship is if you could write it in the traditional form of a line so if you can write it in the Y is equal to MX plus b form where m is the slope of the line and B is the y-intercept so let's see if we can do that well if we want to do that here we could just subtract X from both sides you subtract X from both sides you get so let's subtract an X over here let's subtract an X over here so negative x plus this and then subtract an X there well that's going to cancel and you're going to be left with and I'm going to try to write it in this form right over here y is equal to 45 actually let me do that same color just to make it not be confusing Y is equal to and I'll write the negative x first because we have the X term right over here first so Y is equal to negative x negative x plus 45 plus 45 all I did is I switch these two terms around but you see here it has that form and you might say what is M here I see that B is 45 well if I write negative x that's the same thing as writing negative 1x so this is definitely a line I was able to write it in this form right over here so can this represent this relationship be represented using a linear equation absolutely absolutely yes