That's the reason I some what dis like High School Math ---- it leaves to many blanks.
When the book writes y = something about x. It is describing a function, some times just a relation, but relations are not as fun.
The proper way to do it, let f be a real map (function) from the real numbers to the real numbers (which I assume you are working on the real numbers), denote f:R ---> R
R stands for real.
Then we let y = f(x) for all x. That's what is going on. y is the out come, or the result of the function performed on x. In this case, we multiply x by an arbitrary k. And that's all there is. It means, y is the result of a function on x that involves multiplying x by a factor k.
Ah hah! We say, one formal definition of a function is its graph, the set of all pairs (x, y) where y = f(x). Are they related here? Yes. It is very important (it's the definition) to link them. What the graph looks like is a straight that is tilted in various degree, 0 degree included to 90 degree excluded. As to WHY it look like that, there is a tool called Calculus, which require some proof to figure. If you want to know, ask or message me.
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y = kx: 10 = 37k so k = 10/37 and y = 10x/37
If: kx+y = 4 and y = x^2+8 Then: x^2+8 = 4-kx => x^2+4+kx = 0 For the line to be tangent to the curve the discriminant of b^2-4(ac) must = 0 So: k^2-4(1*4) = 0 => k^2 -16 = 0 => k^2 = 16 => k = +/- 4 Therefore: y+4x = 4 and y-4x = 4 are tangents to the curve y = x^2+8
If you mean: y = kx +1 and y^2 = 8x So if: y = kx +1 then y^2 = k^2*x^2 +2kx +1 If: y^2 = 8x then k^2*x^2 +2kx +1 = 8x Transposing terms: k^2*x^2 +2kx +1 -8x = 0 Using the discriminant: (2k -8)^2 -4*(k^2*1) = 0 Solving the discriminant: k = 2
y=x/7 y=(1/7) x It is a direct variation since it is of the form y=kx, where k=1/7 , a constant
We write y=kx since y varies directly as x. Now we know if x is 5, y is 10. so we write 10=5k so k=2