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CCSS.Math:

graph the line that represents a proportional relationship between y and X with a unit rate 0.4 that is a change of one unit in X corresponds to a change of 0.4 units in Y and they also ask us to figure out what the equation of this line actually is let me get my scratch pad out if we can think about it so let's just think about some potential x and y values here so let's think about some potential x and y values so when we're thinking about proportional relationships that means that Y is going to be equal to some constant times X so if we have a proportional relationship if you have zero X's it doesn't matter what your constant here is you're going to have zero Y's so the point 0 0 should be on your line so this is the point 0 0 this should be on my line right over there now let's think about what happens as we increase X so if X goes from 0 to 1 we already know that a change of one unit in X corresponds to a change of 0.4 units in Y so if x increases by 1 then Y is going to increase by 0.4 it's not so easy to graph this one come as 0.4 0.4 is hard to graph on this on this little tool right over here so let's try to get this to be a whole number so then when x increases another one Y is going to increase by 0.4 again it's going to get to 0.8 when x increases again by 1 then Y is going to increase by 0.4 again it's going to get to 1.2 if x increases again Y is going to increase by 0.4 again so just 1 point 6 notice every time X is increasing by 1 Y is increasing by 0.4 that's exactly what they told us here now if x increases by 1 again to 5 then Y is going to increase 0.422 and I like this point because this is nice and easy to graph so we see that the point 0 0 and the point 5 comma 2 5 comma 2 should be on this graph and I could draw it and I'm going to do it on the tool in a second as well so it looks something something like something like this and notice the slope of this actual graph over here notice the slope of this actual graph if we if our change in X if our change in X five so notice here our change in X is five our change in X is five you see that as well when you go from zero to five your this change in X is five change in X is equal to five what was our corresponding change in Y well our corresponding change in Y when our change in X was five our change in Y was equal to two and you see that here when X went from zero to five Y went from zero to two so our change in Y in this circumstance is equal to two so our slope which is change in Y over change in x over change in X it's the rate of change of your vertical axis with respect to your horizontal axis is going to be equal to it's going to be equal to two over five or 2/5 which if you wrote as the decimal is equal to zero point four so this right over here is your slope so I'm going to do this with the tool but first let's also think about what the equation of this of this line is going to be well we know that Y is equal to some constant times X and we know that the point five two is on this line right over here so we could say well when X is equal to five Y is equal to two or when y equals two we have K times 5 or K is equal to dividing both sides by five dividing both sides by five you can't see that so if I divide both sides by five I'm left with K is equal to 2/5 which makes sense we're used to seeing this when we have Y is equal to something times X this something right over here is going to be our slope so the equation of the line is y is equal to 0.4 X so let's fill this in let's actually do the exercise now so we had two points one was the point zero zero when x is 0 Y is 0 and when X is 5 y is zero point four times that so it's Y is equal to two and we said the equation is y is equal to 0.4 times X so let's check our answer