P is directly proportional to Q. When Q = 6, P = 15. Work out the value of P when Q = 3.5

If P is directly proportional to Q then that means if Q increases P will also increase. If Q decreases P will also decrease. Two values that are directly proportional to each other are related to each other with a proportionality constant. this can be written like this P is directly proportional to Q P =kQ the 'k' represents the proportionality constant now just plug in the first set of information, when Q=6, P=15 15=k x 6 we want to find out the actual value of the constant k, so we rearrange the equation and make k the subject. all we need to do here is divide both sides by 6. 15/6=k now we know the value of the constant! we go back to our original equation and plug in the value of k we found P=kQ P= (15/6)Q Finally, we just need to find P when Q =3.5, so we plug in Q P=(15/6) x 3.5 P =8.75 Now to check our answer with common sense! when Q=6, P was =15. as Q has now DECREASED to 3.5, it makes sense for P to also DECREASE, which indeed it has, from 15 to 8.75!