Hi I'm having trouble with this question I don't understand it at all. This is the question:
Suppose y varies directly with x, and y = 15 and x = 5. Write a direct variation equation that relates x and y. What is the value of y when x = 9?
If somebody could help me & let me know what a direct variation equation is I'll be very grateful to you! I don't know what this is, I missed the last 2 days of school & that must have been when the teacher went over this. My friend tried to help me but he doesn't know what direct variation means either. Thank you if you know anything about this :)))
It's homework due tomorrow & I have practice in an hour so if you can help me before then I'll be so grateful!
Okay I found something on this, so you do 15=5k then divide both sides by 5 to solve for k so you get k=3 then do y=3x but put what they gave, so x=9 so then y=3(9) so is the answer y=27??
x = yk
5 = 15 * 1/3
9 = y * 1/3
Although I use a slightly different process, our answers are the same.
Whenever you have a direct variation of something like
(.....y....) varies directly with (.....x.....) we can say
y = kx
Usually you will be given one case where that is true, in your case x = 5 and y = 15.
So sub that in ...
15 = 5k
k = 3
so now we know the variation equation is y = 3x
The question was : What is the value of y when x = 9?
so let's put in x = 9
y = 3(9) = 27
If the variation is inversely proportional,
we say y = k(1/x) and proceed as before.
Yay, so I was right? Thank you so much
Hi there! I'd be happy to help explain direct variation and how to solve the given question.
Direct variation is a relationship between two variables where one variable is a constant multiple of the other. In other words, as one variable changes, the other changes in proportion to it. It can be represented mathematically as y = kx, where y and x are the variables, and k is the constant of variation.
In this question, we are given that y varies directly with x. We are also given a specific value for y (= 15) when x = 5. We need to write the direct variation equation that relates x and y, and find the value of y when x = 9.
To write the direct variation equation, we need to find the value of the constant of variation (k). We can use the given values of x and y to do this.
Step 1: Plug in the given values of y and x into the equation y = kx.
y = 15
x = 5
Step 2: Solve for k.
15 = k * 5
To isolate k, we divide both sides of the equation by 5:
15/5 = k
Simplifying the equation gives us:
3 = k
Thus, the value of the constant of variation (k) is 3.
Now that we have the value of k, we can rewrite the direct variation equation as:
y = 3x
To find the value of y when x = 9, we can substitute x = 9 into the equation and solve for y.
Substituting x = 9 into y = 3x:
y = 3 * 9
y = 27
Therefore, the value of y when x = 9 is 27.
I hope this explanation helps you understand direct variation and how to solve the given question. If you have any further questions, feel free to ask!