math help?

[Gin Uh Fur]

Write an equation of the line satisfying the given conditions.


Intersects the line y = 2 + 3x at infinitely many places
if someone could EXPLAIN how to do this that be great. you dont have to do it for me. im just sort of lost.

[ThePug]

I believe that it wants the same line. You could rewrite it y = 3x + 2 since it's the same equation.

[Mogget]

The explanation: assuming you're stuck with linear functions (no variables being raised to a power: eg x squared), there are only two ways a line can intersect another line: at one point along the line, or at every point along the line. The only function that will intersect a line at every point along the line, is that selfsame line.

[fragomatrick]

Its easy ! I am an indian ... so math is like supposed to fun for me! Use the straight line formulae and plot it on a graph....... then take out the value of x in terms of y ....and then substitite the value in the above equation to get LHS=RHS!
that value would determine the infinte values this equation can have .....!

[L|L]

A sine function would work, I imagine.

[Mogget]

A sine curve would have to be infinitely tall or tilted (the first isn't possible, the second is insanely difficult). A tangent function would work, but I'm assuming Gin Uh Fur is limited to first-order polynomials.

[Owen]

Originally Posted by Liam

A sine curve would have to be infinitely tall or tilted (the first isn't possible, the second is insanely difficult). A tangent function would work, but I'm assuming Gin Uh Fur is limited to first-order polynomials.

I don't imagine the second option would the that difficult. Why not just have an equation like this: y=2+3x+sin(x). That would intersect the line y=2+3x whenever sin(x) equals zero, and if you go on for infinity, it would be equal to zero at infinitely many places (every multiple of pi).

Originally Posted by Liam

The explanation: assuming you're stuck with linear functions (no variables being raised to a power: eg x squared), there are only two ways a line can intersect another line: at one point along the line, or at every point along the line. The only function that will intersect a line at every point along the line, is that selfsame line.

I don't think that would be a proper intersection, since the second line never deviates from the first line.

Your question asks for an equation of a line. Try drawing any two different lines in the plane. There are only two possibilities: either they are parallel lines, or they intersect at exactly one point.
So no other line has more than one intersection with y = 2 + 3x. Therefore, the only line that intersects it infinitely often is itself.

[Owen]

Originally Posted by Gamer am I

I don't imagine the second option would the that difficult. Why not just have an equation like this: y=2+3x+sin(x). That would intersect the line y=2+3x whenever sin(x) equals zero, and if you go on for infinity, it would be equal to zero at infinitely many places (every multiple of pi).

I suppose I should have added some explanation to my post. For those that aren't familiar with a sine function, the graph of it looks like this:

It extends infinitely in both directions along the x-axis, so that means it wavers between 1 and -1. That means that if you add it to your original function, your new function will waver between being above the original function and below the original function, so it will intersect the function infinitely many times. Here's a graph if you want a visual. I put y=2+3x and y=2+3x+sin(10x) on it. The 10 reduces the wavelength of the sine function, making the intersections more noticeable.

[Ben]

I do fully agree with Gamer am I, but the maths Jennifer takes isn't really advanced enough to be considering anything other than a simple y = mx + c line. =)

Also I always think of the sine wave as boobs standing up for some reason.

[Gin Uh Fur]

thanks guys for all the help :]

[Mogget]

Originally Posted by Ben

I do fully agree with Gamer am I, but the maths Jennifer takes isn't really advanced enough to be considering anything other than a simple y = mx + c line. =)

You learned it y = mx + c? Interesting. I was taught y = mx + b.

[Ben]

Originally Posted by Liam

You learned it y = mx + c? Interesting. I was taught y = mx + b.

Yeah, I guess it's the same thing though. We use + c for the constant after integration and jazz as well~.