1 00:00:00,572 --> 00:00:04,446 y is directly proportional to x. 2 00:00:04,446 --> 00:00:09,798 If y = 30 when x = 6, find the value of x when y = 45. 3 00:00:09,798 --> 00:00:12,526 So let's just take this each statement at a time. 4 00:00:12,526 --> 00:00:14,979 "y is directly proportional to x": 5 00:00:14,979 --> 00:00:20,369 that's literally just saying that y is equal to some constant times x 6 00:00:20,500 --> 00:00:25,185 This statement can literally be translated to y= some constant [writes k] * x. 7 00:00:25,200 --> 00:00:27,322 y is directly proportional to x. 8 00:00:27,322 --> 00:00:32,664 Now they tell us if y = 30 when x = 6 9 00:00:32,664 --> 00:00:36,708 so y is 30 when x is 6 [writes 30 = 6] 10 00:00:36,708 --> 00:00:38,975 And we have this constant of proportionality 11 00:00:38,975 --> 00:00:40,956 This second statement right over here [adds k in space] 12 00:00:40,956 --> 00:00:42,577 allows us to solve for this constant - 13 00:00:42,577 --> 00:00:45,169 when x is 6 it tells us y is 30 14 00:00:45,169 --> 00:00:47,054 so we can figure out what this constant is. 15 00:00:47,054 --> 00:00:51,238 And we can divide both sides by 6 - divide both sides by 6 - 16 00:00:51,238 --> 00:00:56,479 and we get, we get - this left hand side is 5, 30/6 = 5 - 17 00:00:56,479 --> 00:00:58,774 5 = k or k=5 18 00:00:58,774 --> 00:01:04,071 so the second sentence tells us - this gives us the information 19 00:01:04,071 --> 00:01:10,228 that y is not just kx, it tells us that y = 5x. 20 00:01:10,228 --> 00:01:12,559 y is 30 when x is 6. 21 00:01:12,559 --> 00:01:17,867 And then finally, they say find the value of x when y= 45. 22 00:01:17,867 --> 00:01:24,918 So when y is 45, we have 45 is equal to - so this, we're just putting 45 in for y - 23 00:01:24,918 --> 00:01:27,280 45 = 5x 24 00:01:27,280 --> 00:01:30,164 Divide both sides by 5, to solve for x 25 00:01:30,164 --> 00:01:36,510 We get 45/5 is 9. And 5x/5 is just x. 26 00:01:36,510 --> 00:01:43,280 So x is, x = 9 when y=45.