what is the equation of a line perpendicular to 4x+8y=16

Question

anonymous · Answer

A good way to start with these questions is to get it in the form. $$y = mx + c$$Can you do that?

anonymous · Answer

no

anonymous · Answer

No problem, we just need to rearrange our equation. At the moment we have $$4x + 8y = 16$$We can subtract $4x$ from both sides to give $$8y = 16 - 4x$$Now we can divide everything by 8, giving $$y = 2 - 0.5x$$With me so far?

anonymous · Answer

ye

anonymous · Answer

Great! So you can see that the form $$y = mx + c$$is represented by our equation$$y = -0.5x + 2$$We have $m = -0.5$ and $c = 2$

anonymous · Answer

Now another way of saying $0.5$ is the same as $$1\over2$$right?

anonymous · Answer

So we can make our equation $$y = {-1x\over 2} + 2$$Now the gradient of this line is -1/2 which will look something like this|dw:1367505961964:dw|With me so far?

anonymous · Answer

We haven't finished yet, but is there anything so far which doesn't make sense?

anonymous · Answer

I'm going to bed now (I'm in Australia) but the answer is $$y = 2x+c$$where c can be any real number. Because to find the perpendicular of a line you take the inverse reciprocal of the gradient. In our case$${-1 \over 2} \rightarrow 2$$

anonymous · Answer

Hope that helped, please let me know if there is something you don't get.