Question

If y varies directly as x and y=2 when x=-10, find y if x=7.

Answer 1

\(y\) varies directly with \(x\)
\[y(x)\propto x\]
this means there is a constant \(k\) such that
\[y(x)=kx\]

to find \(k\), sub in \(y=2\) when \(x=-10\),

ie \(y(-10)=-10k=2\)

Answer 2

once you have worked out \(k\),

to get \(y\) when \(x=7\),

just compute \(y(7)=7k\)

Answer 3

@Hero Could you please explain?

Answer 4

There is an ideal way to explain this

Answer 5

I'll let @SolomonZelman give it a shot first.

Answer 6

y=kx direct variation
y=2 when x=-10 so
(2)=k(-10)
(-1/5)=k

the variation is -1/5
now find y if
y=(-1/5)7

Answer 7

I'm not good at explaining, sorry.

Answer 8

I don't really need an explanation. What you did was fine. Showing me how to work out the problem is what I wanted explained. Thank you!

Answer 9

Oh, I see, you are similar to me, I can't read a math textbook, but easily follow the unworded work.

Answer 10

Math textbooks are badly organized. That's why. They put the theory and the assignments in the same book.

Answer 11

Almost every textbook I've seen does this.

Answer 12

Yeah, agree.

Answer 13

I think the ideal texbook would have two parts. In the first part, include the theory only. In the second part, include the assignments.

Answer 14

But some people need theory and assignments in the same place.

Answer 15

If they need to do the assignments, they can just flip to the back of the book to do them.

Answer 16

It's wouldn't be that much of a pain to do that

Answer 17

The biggest problem I have with the textbook is they only give a few sample problems. They don't give a sample on all the different problems from each lesson which is hard to learn that way. I am trying to figure out how to do these problems based on the assignment given in the text when I have no idea how to work them out because they don't give good enough of examples. Anyways thanks for the help!