Perpendicular distance between two equations? (parallel)

[Dramacon]

Homework Statement

Find the perpendicular distance between y=2x-1 and y=2x - 8/3


2. The attempt at a solution
The first equation hits the y-axis at -1 and the other at -8/3, which means the vertical (y axis) distance between them is 5/3, but to use trig, I need another piece of information...this is where I am stuck... please help? :)

 

[aeroplane]

Have you tried making a new line y_p perpendicular to both? The segment between the two y lines gives you your perpendicular distance.

 

[SammyS]

Perpendicular distance between two equations? This depends upon where they are written on the page.

Now, to be serious ...

What is the slope of any line that's perpendicular to these two lines?

 

[HallsofIvy]

If SammyS hadn't beaten me to it, I would have said the same- "equations" are not geometric objects. You mean the distance between the two parallel lines that are the graphs, in a given coordinate system, of those two equations.

In any case, as both aeroplane and SammyS have said, find the equation of a line perpendicular to both lines. Find the two points where this third line crosses the two given lines and find the distance between those two points. Since that distance will be the same for any such perpendicular, you can choose whatever point you want for the line to go through.