how do you find the distance between 7x-5y+4=0 and y=7/5x-10?

Question

lgbasallote · Answer

i would like to say the distance between their y intercepts.....

lgbasallote · Answer

|dw:1337130772649:dw| see?

lgbasallote · Answer

so just find the difference then take the absolute value

lgbasallote · Answer

if you wanna know how i found the y-intercepts...it's the constants

anonymous · Answer

The difference -10 and 4 is 14 units. so you wouldn't use the distance formula?

lgbasallote · Answer

well you can....but that is kinda pointless...the coordinates are (0,4) and (0,-10) try the distance formula

lgbasallote · Answer

$$\Large \sqrt{(0 - 0)^2 + (-10 - 4)^2} = \sqrt{14^2} = 14$$

anonymous · Answer

Ahh i'm so slow...ok that make sense. The only thing is that the answers provided are 
a. 6.3
b. 6.28
c.  6.29
d. 6.31

lgbasallote · Answer

hu-what o.O @zepp please help im confused @_@

anonymous · Answer

The question says find the distance between the lines with these equations

anonymous · Answer

but that's what we did.....?

lgbasallote · Answer

so distance between y-intercepts doesnt work =_=

zepp · Answer

Distance between x-intercepts then? o.o

lgbasallote · Answer

|dw:1337131447918:dw|  maybe it should be measured that way..

zepp · Answer

Ohhhh

zepp · Answer

Are those two functions perpendicular? if they are, we can use a perpendicular function that passes through two points.

zepp · Answer

functions parallel*

zepp · Answer

Yup, they are parallel.

zepp · Answer

http://puu.sh/uY4Z

zepp · Answer

@lgbasallote The line you drew between the two functions aren't necessarily perpendicular to these functions

lgbasallote · Answer

that's why i called you :P

zepp · Answer

lol, doing it, had some issue with my calculator's program, hold on >.>

zepp · Answer

Okay, I put those two functions in my calculator: voila: http://puu.sh/uYac

zepp · Answer

Then I need to find the distance, and that distance must be equal for each perpendicular corresponding points (idk how to formulate it but. oh well)

So I'm going to find a function that's perpendicular to those two functions.

zepp · Answer

Now, let's take our slope, 7/5 and twist it, -5/7

zepp · Answer

now you have the slope of the perpendicular function, find the two points and calculate the distance.
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