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Graphing proportional relationships from an equation

CCSS.Math:

Video transcript

we're asked to graph y is equal to 2.5 times X so we really just have to think about two points that satisfy this equation here and the most obvious one is what happens when x equals zero when x equals zero 2.5 times zero is going to be zero so when X is zero Y is going to be equal to zero and then let's just pick another X that will give us a a y that is a whole number so if x increases by 1 Y is going to increase by 2.5 so it's going to go right over there and I could graph it just like that and we see just by just by what I just said that the unit rate of change of Y with respect to X is two point five a unit increase in X a what an increase of 1 and X results in a two point five increase in Y you see that right over here X goes from 0 to 1 Y goes from zero to two point five but let's increase X by another one and then Y is going to increase by two point five again to get to five or you could say look if X is equal to two two point five times two is equal to five so this is a legitimate graph for this equation but then they also tell us to select the statements that are true so the first one is the equation does not represent a proportional relationship well this is a proportional relationship a proportional relationship is one where first of all if you have zero X's you're going to have zero y's where Y is equal to some constant times X and here Y is equal to two point five times X so this is definitely a proportional relationship so I'm not going to check that the unit rate of the relationship is 2/5 so I'm assuming this is a little ambiguous they way they stated it I'm assuming they're saying the unit rate of change of Y with respect to X and the unit rate of change of Y with respect to X is when x increases 1y changed to point five so here they're saying when X changes by 1 Y changes by 0.4 2/5 is the same thing as 0.4 it should be this should be 5 halves 5 halves would be 2.4 so this isn't right as well the slope of the line is 2.5 well this looks right slope is change in Y over change in X when X changes 1 why change is 2.5 so change in y 2.5 over change in X one two point five over one is two point five and you could also see it looking at the form of this equation y is equal to this is the slope times X so that's right a change of five units in X results in a change of two units in Y well let's let's test that idea we know when x is 0 Y is 0 so if X goes from 0 to 5 what's going to happen to Y well Y is going to be 2 point 5 times 5 which is 2 point 5 times 5 is 12 point 5 so Y would not just change two it actually would change 12 point 5 so this isn't right a change in two of two units in X results in a change of five units in Y well we see that a change in two units of X results in a change of five units in Y that's exactly what we graph right over here these two points show that so this is definitely true