Question

Find the distance between each pair of parallel line with the given equations.
y=4x
y=4x-17

Answer 1

Hey there, i've noticed your questions are very similar and was just wondering if you just want answers or to understand the concepts as well?

Answer 2

I could provide help in either case.

Answer 3

I would love very much to understand the concepts mostly because I have another problem dealing with ti so I need to make sure I understand it(:

Answer 4

The important part is that you understand that equations will have equal derivatives when they are parallel. (Same slope, that is to say.) Then you just have to plug in the values you get into simple euclidean distance formula and you're all set!

Answer 5

so in this specific case, the answer is just 17 since slope is constant in the equations of lines.

Answer 6

ooh, that makes a little more sense...

Answer 7

are you in a calculus or algebra class at the moment?

Answer 8

geometry.

Answer 9

ok, so don't be concerned with derivatives. Basically, just plug in values until you can see what each one graphs clearly, and you can literally just count the distance haha

Answer 10

okay okay. lol, so what would be the answer to my other question?

Answer 11

Actually you will see a lot of the form y=mx+b which m is the slope, and as you know that 2 lines are parallel when they have the same slope. So just calculate the difference of the b between those lines. For this question, as you can see, the first function has the slope 4 as well as the second function, but the first function has b=0 , the second one has b=-17. So the difference between them are 17. By the way, you should always have the absolute value for the distance. Hope you can get some idea from this.

Answer 12

\[\tan\alpha=4\]\[d_\perp=d_0\cdot\cos\alpha\quad;\quad d_0=17\quad,\quad\cos\alpha=\frac{1}{\sqrt{1+\tan^2\alpha}}=\frac{1}{\sqrt{17}}\]\[d_\perp=17\cdot\frac{1}{\sqrt{17}}=\sqrt{17}\]