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正比的比值 (英): 正比的比值
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- y is directly proportional to x.
- If y = 30 when x = 6, find the value of x when y = 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= some constant [writes k] * x.
- y is directly proportional to x.
- Now they tell us if y = 30 when x = 6
- so y is 30 when x is 6 [writes 30 = <space> 6]
- And we have this constant of proportionality
- This second statement right over here [adds k in space]
- allows us to solve for this constant -
- when x is 6 it tells us y 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, 30/6 = 5 -
- 5 = k or k=5
- so the second sentence tells us - this gives us the information
- that y is not just k*x, it tells us that y = 5*x.
- y is 30 when x is 6.
- And then finally, they say find the value of x when y= 45.
- So when y is 45, we have 45 is equal to - so this, we're just putting 45 in for y -
- 45 = 5x
- Divide both sides by 5, to solve for x
- We get 45/5 is 9. And 5x/5 is just x.
- So x is, x = 9 when y=45.
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