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why is directly proportional to X if y equals 30 when X is equal to 6 find the value of x when y is 45 so let's just take this each statement at a time Y is directly proportional to X that's literally just saying that Y is equal to some constant times X this statement can literally be translated to Y is equal to some constant times X Y is directly proportional to X now they tell us if Y is 30 when X is 6 so Y is 30 when X is 6 and we have this constant of proportionality the second statement right over here allows us to solve for this constant when X is 6 they tell us why is 30 so we can figure out what this constant is and we can divide both sides by 6 divide both sides by 6 and we get we get this left-hand side is 5 30 divided by 6 is 5 5 is equal to K or K is equal to 5 so the second sentence test the second sentence tells us this gives us the information that Y is not just K times X it tells us that Y is equal to 5 times X Y is 30 when X is 6 and then finally they say find the value of x when y is 45 so when y is 45 we have 45 is equal to so this is we're just putting in 45 for y 45 is equal to 5 X divide both sides by 5 to solve for X we get 45 over 5 is 9 and + 5 X divided by 5 is just X so X is X is equal to 9 when y is 45